#polyhedron — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #polyhedron, aggregated by home.social.
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This version omits the square faces so that we can inside the prisms
13/n
#geogebra #geometry #origami #design #MathArt #MastoArt #FediArt #CreativeToots #animation #loop #Procedural #polyhedron #polyhedra
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This version omits the square faces so that we can inside the prisms
13/n
#geogebra #geometry #origami #design #MathArt #MastoArt #FediArt #CreativeToots #animation #loop #Procedural #polyhedron #polyhedra
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And here's a skeletal octahedron transforming into three cuboids (and back again).
Even though this seems easier to visualise, I find some of the configurations fascinating, especially the three cuboids when three edges meet at common points, and the three cubes.
12/n
#geogebra #geometry #origami #design #MathArt #MastoArt #FediArt #CreativeToots #animation #loop #Procedural #polyhedron #polyhedra
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And here's a skeletal octahedron transforming into three cuboids (and back again).
Even though this seems easier to visualise, I find some of the configurations fascinating, especially the three cuboids when three edges meet at common points, and the three cubes.
12/n
#geogebra #geometry #origami #design #MathArt #MastoArt #FediArt #CreativeToots #animation #loop #Procedural #polyhedron #polyhedra
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#Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt
The video in this post by @graveolensa
https://mathstodon.xyz/@graveolensa/115885487505867437
about people with 4 color cones having a sphere's worth of hues is fascinating but, being a trichromat, i don't fully understand it or know if its correct. Here is a mathematically simple but scientifically crude analogy between trichromaticity and tetrachromaticity.
A note on the figures, although this is about color vision and the figures have been colored the colors in the figures are just rough guides for trichromats, which most people are. This analogy is too crude for the colors to precisely match a trichromat's color experiences.
The visible spectrum is rounded off to the interval [415 THz, 715 THz]. The cone cells' activation, as a function of the frequency of monochromatic light they receive, are idealized to the piecewise linear spectral sensitivity curves shown in the figure. They are surjective to \([0,1]\) so as to implement Ooqui's "rule of hue". Call them \(r(\nu)\) (red cone), \(g(\nu)\) (green cone), and \(b(\nu)\) (violet cone).
Each cone type has exactly 1 frequency of monochromatic light where it is the only type of cone that is activated and that cone's activation is 1 at that frequency. These frequencies are 415, 565, and 715. At every other frequency in the visible spectrum exactly 2 cone types are activated by monochromatic light and the activation of at least one of them is 1.
(1/6)
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#Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt
The video in this post by @graveolensa
https://mathstodon.xyz/@graveolensa/115885487505867437
about people with 4 color cones having a sphere's worth of hues is fascinating but, being a trichromat, i don't fully understand it or know if its correct. Here is a mathematically simple but scientifically crude analogy between trichromaticity and tetrachromaticity.
A note on the figures, although this is about color vision and the figures have been colored the colors in the figures are just rough guides for trichromats, which most people are. This analogy is too crude for the colors to precisely match a trichromat's color experiences.
The visible spectrum is rounded off to the interval [415 THz, 715 THz]. The cone cells' activation, as a function of the frequency of monochromatic light they receive, are idealized to the piecewise linear spectral sensitivity curves shown in the figure. They are surjective to \([0,1]\) so as to implement Ooqui's "rule of hue". Call them \(r(\nu)\) (red cone), \(g(\nu)\) (green cone), and \(b(\nu)\) (violet cone).
Each cone type has exactly 1 frequency of monochromatic light where it is the only type of cone that is activated and that cone's activation is 1 at that frequency. These frequencies are 415, 565, and 715. At every other frequency in the visible spectrum exactly 2 cone types are activated by monochromatic light and the activation of at least one of them is 1.
(1/6)
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I am ready to admit defeat!
This is a partial collapse of the Gamma Star model by John Montroll.
I've stopped on step 58 of 61. Sad, but it's not going to come together.
His one-sheet origami polyhedra models are some of the hardest collapses I know. Anyone done this with success?
I am using 50 X 50 cm 300gsm watercolour paper, which is completely wrong and silly, but I like the challenge. Even the pre-creasing took hours....
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I am ready to admit defeat!
This is a partial collapse of the Gamma Star model by John Montroll.
I've stopped on step 58 of 61. Sad, but it's not going to come together.
His one-sheet origami polyhedra models are some of the hardest collapses I know. Anyone done this with success?
I am using 50 X 50 cm 300gsm watercolour paper, which is completely wrong and silly, but I like the challenge. Even the pre-creasing took hours....
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Luca Pacioli’s (c.1445–1517) book ‘Divina proportione’ (written 1496–8, published 1509) is famous in the history of mathematical beauty, but mostly for the wrong reasons.
The term ‘divine proportion’ refers to Euclid's ‘extreme and mean ratio’, known since the late 18th century as the ‘golden ratio’: $1.61803\ldots:1$.
Pacioli's use of the term ‘divine’ **was not based upon aesthetic appreciation**.
Rather, he made a mystical identification of certain properties of the ratio with attributes of God. E.g., the incommensurability of the ratio = the indefinability and ineffability of God.
But Pacioli aesthetically admired the five regular polyhedra — the platonic solids — and the archimedean solids that he knew. In the dedication of ‘Divina proportione’ he wrote that hoped that his patron would see ‘their most sweet harmony’. He linked the aesthetic value of the solids to that of the sphere, from which he saw them as deriving. He seems to have placed special value on the ‘most noble’ dodecahedron.
In his portrait (attached), a dodecahedron sits on top of one of his books as a symbol of mathematical success. His diagram is part of the construction of the tetrahedron. A glass rhombicuboctahedron hangs behind him.
1/3
[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]
#GoldenRatio #DivineProportion #MathematicalBeauty #MathArt #polyhedron #RegularSolid #PlatonicSolid
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Luca Pacioli’s (c.1445–1517) book ‘Divina proportione’ (written 1496–8, published 1509) is famous in the history of mathematical beauty, but mostly for the wrong reasons.
The term ‘divine proportion’ refers to Euclid's ‘extreme and mean ratio’, known since the late 18th century as the ‘golden ratio’: $1.61803\ldots:1$.
Pacioli's use of the term ‘divine’ **was not based upon aesthetic appreciation**.
Rather, he made a mystical identification of certain properties of the ratio with attributes of God. E.g., the incommensurability of the ratio = the indefinability and ineffability of God.
But Pacioli aesthetically admired the five regular polyhedra — the platonic solids — and the archimedean solids that he knew. In the dedication of ‘Divina proportione’ he wrote that hoped that his patron would see ‘their most sweet harmony’. He linked the aesthetic value of the solids to that of the sphere, from which he saw them as deriving. He seems to have placed special value on the ‘most noble’ dodecahedron.
In his portrait (attached), a dodecahedron sits on top of one of his books as a symbol of mathematical success. His diagram is part of the construction of the tetrahedron. A glass rhombicuboctahedron hangs behind him.
1/3
[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]
#GoldenRatio #DivineProportion #MathematicalBeauty #MathArt #polyhedron #RegularSolid #PlatonicSolid
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Pure #CSS #3D chamfering sequence on @codepen cube → chamfered cube → rhombic dodecahedron and back
https://codepen.io/thebabydino/pen/rNdjLdq
Chamfer? WTF is that?
Well, check out the Pen description https://codepen.io/thebabydino/details/rNdjLdq and this page https://en.wikipedia.org/wiki/Chamfer_(geometry)
#Maths #geometry #css3D #transform #chamfer #polyhedron #polyhedra #cube #rhombicDodecahedron #code #coding #web #dev #webDev #webDevelopment
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Pure #CSS #3D chamfering sequence on @codepen cube → chamfered cube → rhombic dodecahedron and back
https://codepen.io/thebabydino/pen/rNdjLdq
Chamfer? WTF is that?
Well, check out the Pen description https://codepen.io/thebabydino/details/rNdjLdq and this page https://en.wikipedia.org/wiki/Chamfer_(geometry)
#Maths #geometry #css3D #transform #chamfer #polyhedron #polyhedra #cube #rhombicDodecahedron #code #coding #web #dev #webDev #webDevelopment
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Pure #CSS #3D demo on @codepen: polyhedra morphing sequence https://codepen.io/thebabydino/pen/abmNveW
Absolutely no magic numbers, everything computed.
See Pen description for the how behind 😼
#transform #cssTransform #polyhedron #cssTransforms #polyhedra #octahedron #tetrahedron #cube #Maths #geometry #cssVariables #code #coding #frontend #web #dev #webDev #webDevelopment
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Pure #CSS #3D demo on @codepen: polyhedra morphing sequence https://codepen.io/thebabydino/pen/abmNveW
Absolutely no magic numbers, everything computed.
See Pen description for the how behind 😼
#transform #cssTransform #polyhedron #cssTransforms #polyhedra #octahedron #tetrahedron #cube #Maths #geometry #cssVariables #code #coding #frontend #web #dev #webDev #webDevelopment
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Exploding triakis octahedron (short pyramids added on top of the faces) turning into an excavated octahedron (short pyramids dug into the faces) with pure #CSS #3D - live on @codepen: https://codepen.io/thebabydino/pen/DyrNrL
#Maths #geometry #polyhedra #css3D #cssTransform #cssTransforms #coding #code #transform #frontend #cssMaths #Sass #web #dev #webDevelopment #webDev #trigonometry #polyhedron #octahedron
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Exploding triakis octahedron (short pyramids added on top of the faces) turning into an excavated octahedron (short pyramids dug into the faces) with pure #CSS #3D - live on @codepen: https://codepen.io/thebabydino/pen/DyrNrL
#Maths #geometry #polyhedra #css3D #cssTransform #cssTransforms #coding #code #transform #frontend #cssMaths #Sass #web #dev #webDevelopment #webDev #trigonometry #polyhedron #octahedron
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One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron https://codepen.io/thebabydino/pen/ALQVQe
A dodecahedron is one of the 5 regular polyhedra = made up of only identical regular polygon faces. Regular polygons have all edge lengths and vertex angles equal.
#geometry #Maths #code #coding #css3D #cssTransforms #transform #frontend #polyhedron #polyhedra #PlatonicSolid #dodecahedron #cssAnimation #web #dev #webDev #webDevelopment #trigonometry #Sass #SCSS
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One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron https://codepen.io/thebabydino/pen/ALQVQe
A dodecahedron is one of the 5 regular polyhedra = made up of only identical regular polygon faces. Regular polygons have all edge lengths and vertex angles equal.
#geometry #Maths #code #coding #css3D #cssTransforms #transform #frontend #polyhedron #polyhedra #PlatonicSolid #dodecahedron #cssAnimation #web #dev #webDev #webDevelopment #trigonometry #Sass #SCSS
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@scdollins Excellent, I’m now trying to visualise a construction starting from the icosahedron...
A straightforward solution from an icosahedron: add two octahedra and a tetrahedron on each face of the icosahedron to get 20 * 15 faces.
Yes, the faces of the tetrahedra and octahedra merge as rhombic face, but Hedron App @hedron counts distinct faces (the tetrahedra could be distorted to make 3 distinct faces.)
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@scdollins Excellent, I’m now trying to visualise a construction starting from the icosahedron...
A straightforward solution from an icosahedron: add two octahedra and a tetrahedron on each face of the icosahedron to get 20 * 15 faces.
Yes, the faces of the tetrahedra and octahedra merge as rhombic face, but Hedron App @hedron counts distinct faces (the tetrahedra could be distorted to make 3 distinct faces.)
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@obot50549535
Apparently the compound of ten tetrahedra has 300 edges (when counted as non-intersecting).Also, some octahedral geodesic polyhedra and Goldberg polyhedra have 300 edges: u5O and c5C at https://en.wikipedia.org/wiki/List_of_geodesic_polyhedra_and_Goldberg_polyhedra#Octahedral
Nice, but still looking for 300 faces (or vertices)...
#askfedi #mathematics #geometry #iTeachMath #polyhedron #geodesic
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@obot50549535
Apparently the compound of ten tetrahedra has 300 edges (when counted as non-intersecting).Also, some octahedral geodesic polyhedra and Goldberg polyhedra have 300 edges: u5O and c5C at https://en.wikipedia.org/wiki/List_of_geodesic_polyhedra_and_Goldberg_polyhedra#Octahedral
Nice, but still looking for 300 faces (or vertices)...
#askfedi #mathematics #geometry #iTeachMath #polyhedron #geodesic
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Do you know a polyhedron that has 300 faces? Ideally nice and non-trivial.
Or a polyhedron with 300 edges or 300 vertices?
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Do you know a polyhedron that has 300 faces? Ideally nice and non-trivial.
Or a polyhedron with 300 edges or 300 vertices?
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Something newer: an elegant "almost orthogonal polyhedron: a polyhedron whose adjacent faces are orthogonal to each other, except on one edge." https://www.gathering4gardner.org/g4g15gift/ExchangeArchive-AlmostOrthogonalPolyhedra-G15-093-1.pdf
h/t @robinhouston
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Something newer: an elegant "almost orthogonal polyhedron: a polyhedron whose adjacent faces are orthogonal to each other, except on one edge." https://www.gathering4gardner.org/g4g15gift/ExchangeArchive-AlmostOrthogonalPolyhedra-G15-093-1.pdf
h/t @robinhouston
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A ring of five cubes cut and joined in Geogebra.
You can see the approximation’s fault on the right. With paper models, the error is less noticeable.
The dodecahedral version with 30 cubes is harder to model as Craig Kaplan has noted: "because you can let the laws of physics absorb and distribute the mathematical error inherent in the [physical] construction. To build a computer model, you must make explicit decisions about where that error should go. For example, the faces could be made slightly irregular, or slightly non-planar." https://isohedral.ca/a-molecular-near-miss
h/t Dave Mitchell (modular origami Columbus Cube, Ring of Cubes and Ball of Cubes http://www.origamiheaven.com/pdfs/columbus.pdf)
edit: add link to origami instruction
#mathtober #mathtober3 #polyhedron #cube #design #geometry #MathArt #geogebra #origami
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A ring of five cubes cut and joined in Geogebra.
You can see the approximation’s fault on the right. With paper models, the error is less noticeable.
The dodecahedral version with 30 cubes is harder to model as Craig Kaplan has noted: "because you can let the laws of physics absorb and distribute the mathematical error inherent in the [physical] construction. To build a computer model, you must make explicit decisions about where that error should go. For example, the faces could be made slightly irregular, or slightly non-planar." https://isohedral.ca/a-molecular-near-miss
h/t Dave Mitchell (modular origami Columbus Cube, Ring of Cubes and Ball of Cubes http://www.origamiheaven.com/pdfs/columbus.pdf)
edit: add link to origami instruction
#mathtober #mathtober3 #polyhedron #cube #design #geometry #MathArt #geogebra #origami
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A modular origami cube and a stella octangula. Each uses different units.
The stella octangula is a stellated regular octahedron and also the compound of two regular tetrahedra. It fits neatly inside a cube. https://en.wikipedia.org/wiki/Stellated_octahedron
From the exhibition "‘A Wonderful World, organised by the Embassy of Japan in Việt Nam and the Việt Nam Origami Group (VOG)’ … [showing works by] Mitya Miller, Nicolas Terry, and Tung Ken Lam, alongside new creations from VOG unveiled especially for the exhibition. … The exhibition runs until October 10 on the 4th floor, Gate C, at the Embassy of Japan, 27 Liễu Giai Street, with free admission." https://vietnamnews.vn/life-style/1726153/folding-fun-as-origami-art-springs-to-life.html
Image courtesy of VOG
#mathtober #polyhedron #origami #design #craft #Papercraft #photography #geometry #design #MathArt #ArtistOnMastodon #ArtistsOnMastodon #artwork #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots #MathsArt #vietnam #exhibition #hanoi
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A modular origami cube and a stella octangula. Each uses different units.
The stella octangula is a stellated regular octahedron and also the compound of two regular tetrahedra. It fits neatly inside a cube. https://en.wikipedia.org/wiki/Stellated_octahedron
From the exhibition "‘A Wonderful World, organised by the Embassy of Japan in Việt Nam and the Việt Nam Origami Group (VOG)’ … [showing works by] Mitya Miller, Nicolas Terry, and Tung Ken Lam, alongside new creations from VOG unveiled especially for the exhibition. … The exhibition runs until October 10 on the 4th floor, Gate C, at the Embassy of Japan, 27 Liễu Giai Street, with free admission." https://vietnamnews.vn/life-style/1726153/folding-fun-as-origami-art-springs-to-life.html
Image courtesy of VOG
#mathtober #polyhedron #origami #design #craft #Papercraft #photography #geometry #design #MathArt #ArtistOnMastodon #ArtistsOnMastodon #artwork #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots #MathsArt #vietnam #exhibition #hanoi
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It's late and I spent some time to do the estimation experiment (https://mastodon.de/@gwenbeads@mathstodon.xyz/115312008857653097 - I actually came to 5 cups but I chose to say 'D12' from the beginning...)
So this has to do as my contribution for #mathober day 3: #polyhedron
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It's late and I spent some time to do the estimation experiment (https://mastodon.de/@gwenbeads@mathstodon.xyz/115312008857653097 - I actually came to 5 cups but I chose to say 'D12' from the beginning...)
So this has to do as my contribution for #mathober day 3: #polyhedron
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Polyhedron - #mathober day 3
#polyhedron #mathober2025 #mtbos #mathart #pnw #birds #birdart
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Polyhedron - #mathober day 3
#polyhedron #mathober2025 #mtbos #mathart #pnw #birds #birdart
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The #Mathober day 3 prompt is ‘#Polyhedron’. I have no art to offer, but I thought I would use the occasion to draw attention to a lesser-known role of polyhedra in Johannes Kepler's (1571–1630) thought.
Start with the famous part: Kepler argued that the five regular (or Platonic) solids fitted between the orbs of the then-known six planets [https://commons.wikimedia.org/wiki/File:Kepler-solar-system-1.png].
When Galileo discovered four moons of Jupiter, Kepler sought a similar polyhedral structure for the Jovian system, and suggested that ‘semiregular’ solids provided the key. ‘Semiregular’ for Kepler meant that the polyhedra had rhombic faces and satisfied certain technical criteria. (The concept differs from today's notion of semiregular polyhedra.)
There were exactly three such ‘semiregular’ polyhedra:
• the cube (the square being a special kind of rhombus).
• the rhombic dodecahedron (12 faces; diagram attached).
• the rhombic triacontahedron (30 faces; diagram attached).
Kepler placed the rhombic dodecahedron between Io and Europa, the rhombic triacontahedron between Europa and Ganymede, and the cube between Ganymede and Callisto.
Kepler thought that there were six planets because God had shaped the cosmos around the five platonic solids. The three ‘semiregular’ solids would similarly explain why there were four moons of Jupiter.
Perhaps someone who is a better artist than I am could draw a diagram of the three rhombic solids and the orbs of the four Galilean moons in the style of Kepler's famous diagram of the Platonic solids between the orbs of the planets.
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The #Mathober day 3 prompt is ‘#Polyhedron’. I have no art to offer, but I thought I would use the occasion to draw attention to a lesser-known role of polyhedra in Johannes Kepler's (1571–1630) thought.
Start with the famous part: Kepler argued that the five regular (or Platonic) solids fitted between the orbs of the then-known six planets [https://commons.wikimedia.org/wiki/File:Kepler-solar-system-1.png].
When Galileo discovered four moons of Jupiter, Kepler sought a similar polyhedral structure for the Jovian system, and suggested that ‘semiregular’ solids provided the key. ‘Semiregular’ for Kepler meant that the polyhedra had rhombic faces and satisfied certain technical criteria. (The concept differs from today's notion of semiregular polyhedra.)
There were exactly three such ‘semiregular’ polyhedra:
• the cube (the square being a special kind of rhombus).
• the rhombic dodecahedron (12 faces; diagram attached).
• the rhombic triacontahedron (30 faces; diagram attached).
Kepler placed the rhombic dodecahedron between Io and Europa, the rhombic triacontahedron between Europa and Ganymede, and the cube between Ganymede and Callisto.
Kepler thought that there were six planets because God had shaped the cosmos around the five platonic solids. The three ‘semiregular’ solids would similarly explain why there were four moons of Jupiter.
Perhaps someone who is a better artist than I am could draw a diagram of the three rhombic solids and the orbs of the four Galilean moons in the style of Kepler's famous diagram of the Platonic solids between the orbs of the planets.
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🎉 Breaking news from the math world: someone found a #polyhedron that doesn't care about Rupert's property! 🔍🤓 Apparently, this is so #groundbreaking that it required an entire #research paper, because who doesn't love a good polyhedron drama? 🙃🧮
https://arxiv.org/abs/2508.18475 #mathnews #RupertProperty #mathdrama #HackerNews #ngated -
🎉 Breaking news from the math world: someone found a #polyhedron that doesn't care about Rupert's property! 🔍🤓 Apparently, this is so #groundbreaking that it required an entire #research paper, because who doesn't love a good polyhedron drama? 🙃🧮
https://arxiv.org/abs/2508.18475 #mathnews #RupertProperty #mathdrama #HackerNews #ngated -
Here’s the other side, part- and fully-assembled. Some units don’t fit as well as the front side.
I guess the 90-unit QRSTUVWXYZ (10 nine-pointed stars) is next?
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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Here’s the other side, part- and fully-assembled. Some units don’t fit as well as the front side.
I guess the 90-unit QRSTUVWXYZ (10 nine-pointed stars) is next?
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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And the 56-unit RSTUVWXYZ Stars: eight intersecting seven-pointed stars.
Modular origami folded from 5:4 rectangles cut from eight sheets of colour A4 paper.
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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And the 56-unit RSTUVWXYZ Stars: eight intersecting seven-pointed stars.
Modular origami folded from 5:4 rectangles cut from eight sheets of colour A4 paper.
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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Here’s the other side, part- and fully-assembled.
Made from 72 sheets of 10 cm Paperchase Spectrascope memo block paper squares.#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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Here’s the other side, part- and fully-assembled.
Made from 72 sheets of 10 cm Paperchase Spectrascope memo block paper squares.#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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Turns out RSTUVWXYZ Stars (72 units, nine intersecting eight-pointed stars) was easier to assemble as it the connections are more stable, as is the final result.
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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Turns out RSTUVWXYZ Stars (72 units, nine intersecting eight-pointed stars) was easier to assemble as it the connections are more stable, as is the final result.
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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Here’s the other side, part- and fully-assembled.
I have an idea for RSTUVWXYZ Stars (72 units, nine intersecting eight-pointed stars) which will take some time. Even though it has more units, it has easier geometry than STUVWXYZ Stars (56 units, eight intersecting seven-pointed stars).
Meenakshi Mukerji called these ‘unconventional polyhedra’ 😆
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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Here’s the other side, part- and fully-assembled.
I have an idea for RSTUVWXYZ Stars (72 units, nine intersecting eight-pointed stars) which will take some time. Even though it has more units, it has easier geometry than STUVWXYZ Stars (56 units, eight intersecting seven-pointed stars).
Meenakshi Mukerji called these ‘unconventional polyhedra’ 😆
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
#star #origami #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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A few different folds adapts the unit for TUVWXYZ Stars, a modular origami model of seven intersecting six-pointed stars.
Made from seven sheets of A4 colour paper, each cut into six 1:√3 rectangles, fold and joined without glue.
How can there be 42 units? See Meenakshi Mukerji’s guide to planar modulars at https://origamee.net/diagrams/planars (which I’ve only just found, after all these years)
#star #origami #FotoMontag #PhotoMonday #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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A few different folds adapts the unit for TUVWXYZ Stars, a modular origami model of seven intersecting six-pointed stars.
Made from seven sheets of A4 colour paper, each cut into six 1:√3 rectangles, fold and joined without glue.
How can there be 42 units? See Meenakshi Mukerji’s guide to planar modulars at https://origamee.net/diagrams/planars (which I’ve only just found, after all these years)
#star #origami #FotoMontag #PhotoMonday #MathArt #geometry #polyhedron #ModularOrigami #craft #design #PaperCraft #photography #ArtistOnMastodon #ArtistsOnMastodon #artwork #3D #art #artist #arts #arte #designer #MastoArt #FediArt #CreativeToots
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@rasjor @nanma80 Geogebra has a Net tool/command, but it lacks flexibility -- I guess the dedicated could edit the source code
https://geogebra.github.io/docs/manual/en/tools/Net/
#geogebra #geometry #dodecahedron #animation #loop #polyhedron -
@rasjor @nanma80 Geogebra has a Net tool/command, but it lacks flexibility -- I guess the dedicated could edit the source code
https://geogebra.github.io/docs/manual/en/tools/Net/
#geogebra #geometry #dodecahedron #animation #loop #polyhedron -
Truncated ‘cuboctahedron’ mapped from continuous polynomial x^80+y^80+z^80+.6133^80((y+z)^80+(z+x)^80+(x+y)^80+(y-z)^80+(z-x)^80+(x-y)^80)+.5286^80((x+y+z)^80+(x+y-z)^80+(x-y+z)^80+(-x+y+z)^80)-1=0. An Archimedean solid, it has 26 regular faces (6 octagonal, 8 hexagonal and 12 square), 48 vertices and 72 equal edges. It is not a true truncation of the cuboctahedron which instead results in 12 rectangular faces rather than square. However, with a bit of (mathematical) stretching, the requisite all edges equal condition can be met. #Maths #Mathematics #Math #polyhedron
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Perfect fit.