Toby Schachman

@mandy3284

Making CAD tools. Previously

Vrijeme pridruživanja: svibanj 2009.

Medijski sadržaj

  1. 30. lis 2019.

    Last chance to get your Sun Seed Kit 🌈✨ Our campaign ends at midnight! Thank you everyone who has pledged and shared and supported our art! 💗

  2. 29. lis 2019.

    Deep analysis argues that US can 100% decarbonize with existing tech: electric vehicles, heat pumps, solar on every roof, etc. These changes will pay for themselves in time due to greater efficiency, just needs to be coordinated and financed.

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  3. 29. lis 2019.

    The CA fires and PG&E bankruptcy is an opportunity to rethink our power grid. Properly accounting for the externalities of power transmission make local renewables, storage, and microgrids more attractive. Best intro I've read on this subject, by

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  4. 28. lis 2019.
    Odgovor korisniku/ci

    It's always great to find more ways of seeing the shapes and how they can be constructed! I *think* you can make all the Archimedean Solids with truncation (like the above animation), expansion (below), and that snub operation.

  5. 28. lis 2019.
    Odgovor korisnicima

    I'm not sure how you can get the "snub" shapes with this strategy though. These necessarily involve a "twist" and indeed the snub shapes are chiral (have a handedness). Here's a snub cube and snub dodecahedron:

  6. 28. lis 2019.
    Odgovor korisniku/ci

    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 dodecahedron

  7. 28. lis 2019.
    Odgovor korisnicima

    A d10 is a Trapezohedron These aren't traditionally considered Catalan Solids but they arguably should be because they satisfy the properties: ✅ Faces are identical ✅ Angles around any vertex are equal

  8. 28. lis 2019.

    ⚡️ We are making a small batch of Sun Seed Kits! 🌈 Check it out if you're interested in making your own color-changing, geometric sculptures. Our crowdfund ends in 2 days!

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  9. 28. lis 2019.

    The "Lotus" Sun Seed, designed by , 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.

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  10. 28. lis 2019.

    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?

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  11. 28. lis 2019.

    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.

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  12. 28. lis 2019.

    I came upon the Catalan Solids while working on "Sun Seeds", a sculpture collaboration with and .

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  13. 28. lis 2019.

    ❌ 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!

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  14. 28. lis 2019.

    ✅ 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.

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  15. 28. lis 2019.

    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).

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  16. 28. lis 2019.

    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 equal

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  17. 28. lis 2019.

    Here's an animation showing an icosahedron transforming into a dodecahedron and back again.

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  18. 28. lis 2019.

    The dual of an icosahedron (20 faces, 12 vertices) is a dodecahedron (12 faces, 20 vertices).

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  19. 28. lis 2019.

    Here's an animation showing a cube transforming into an octahedron and back again.

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  20. 28. lis 2019.

    The dual of a cube is an octahedron. A cube has 6 faces and 8 vertices. An octahedron has 8 faces and 6 vertices. You replace every face by a vertex, and every vertex by a face.

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