Here's an animation showing an icosahedron transforming into a dodecahedron and back again.pic.twitter.com/X0eGEItLzz
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If you take the duals of the 13 Archimedean Solids, you get the 13 Catalan Solids! Because we're swapping faces with vertices, all the properties also swap!
Faces are identical
Vertices are identical
Faces are regular polygons
Angles around any vertex are equalpic.twitter.com/UT9LY0imL7
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For example, the dual of the icosidodecahedron (an Archimedean Solid with 32 faces and 30 vertices) is the rhombic triacontahedron (a Catalan Solid with 30 faces and 32 vertices).pic.twitter.com/zBK92I6k3e
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Faces are identical
Faces are regular polygons
On the rhombic triacontahedron, the faces are all the same but they're no longer regular, in this case they're a rhombus (diamond) shape.pic.twitter.com/Z9D4vb1Oiw
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Vertices are identical
Angles around any vertex are equal
At every vertex, the angles go around regularly. But there are two classes of vertices, those where 5 shapes meet and those where 3 shapes meet. These correspond to the pentagons and triangles of the dual!pic.twitter.com/OJCFNLwfuX
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I came upon the Catalan Solids while working on "Sun Seeds", a sculpture collaboration with
@mokeymuffin and@notlion.pic.twitter.com/mloEJDCNIP1 reply 0 proslijeđenih tweetova 1 korisnik označava da mu se sviđaPrikaži ovu nit -
The properties of the Catalan Solids were perfect for evoking the symmetries of flowers and microscopic plant life that inspired our project. Below is an electron microscope image of pollen from a variety of plants.pic.twitter.com/v6ehHdbWtq
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I based my "Mint" Sun Seed on the rhombic triacontahedron. There are 30 identical pieces. Every vertex is a flower. Can you find the big flowers with 5 petals and the small ones with 3 petals?pic.twitter.com/J3vHf4dM9m
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The "Lotus" Sun Seed, designed by
@mokeymuffin, is based on the pentagonal hexecontahedron. It has 12 large flowers where 5 pieces come together and 80 small flowers where 3 pieces come together.pic.twitter.com/DtI9FM6HpL
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We are making a small batch of Sun Seed Kits!
https://www.indiegogo.com/projects/sun-seeds/ …
Check it out if you're interested in making your own color-changing, geometric sculptures. Our crowdfund ends in 2 days!pic.twitter.com/hrPMmiPFzC1 reply 0 proslijeđenih tweetova 3 korisnika označavaju da im se sviđaPrikaži ovu nit
I hope you enjoyed this introduction to the Catalan Solids, Platonic Solids, Archimedean Solids, and the concept of "dual" shapes. You can read more on Wikipedia https://en.wikipedia.org/wiki/Catalan_solid … The GIFs showing a shape turning into its dual came from this page https://www.antiprism.com/album/815_truncations/imagelist.html …
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Odgovor korisniku/ci @mandy3284
I always thought of them as the interim stage of transformaction between Platonic duals as you raise a vertex in the centre of each face. Extras come from convergence with an adjacent.
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Odgovor korisniku/ci @mattjohns
I can definitely see many of the Archimedean Solids as the interim stage of a transformation between Platonic duals, for example icosidodecahedron is halfway between icosahedron and dodecahedronpic.twitter.com/Xj9csdoU07
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