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#polyhedron — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #polyhedron, aggregated by home.social.

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt

    The video in this post by @graveolensa

    mathstodon.xyz/@graveolensa/11

    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)

  7. #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt

    The video in this post by @graveolensa

    mathstodon.xyz/@graveolensa/11

    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)

  8. #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt

    The video in this post by @graveolensa

    mathstodon.xyz/@graveolensa/11

    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)

  9. #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt

    The video in this post by @graveolensa

    mathstodon.xyz/@graveolensa/11

    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)

  10. #Polyhedron #Polygons #tiles #opticalillusion #MathArt #MathsArt

    The video in this post by @graveolensa

    mathstodon.xyz/@graveolensa/11

    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)

  11. 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....

    #origami #polyhedron

  12. 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....

    #origami #polyhedron

  13. 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....

    #origami #polyhedron

  14. 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....

    #origami #polyhedron

  15. 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....

    #origami #polyhedron

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron codepen.io/thebabydino/pen/ALQ

    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

  22. One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron codepen.io/thebabydino/pen/ALQ

    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

  23. One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron codepen.io/thebabydino/pen/ALQ

    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

  24. One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron codepen.io/thebabydino/pen/ALQ

    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

  25. One of my earliest #CSS #3D demos on @codepen: how to (de)construct a dodecahedron codepen.io/thebabydino/pen/ALQ

    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

  26. @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.)

    #mathematics #geometry #polyhedron #3d

  27. @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.)

    #mathematics #geometry #polyhedron #3d

  28. @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.)

    #mathematics #geometry #polyhedron #3d

  29. @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.)

    #mathematics #geometry #polyhedron #3d

  30. @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.)

    #mathematics #geometry #polyhedron #3d