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# Clayton Shonkwiler @shonk@mathstodon.xyz

Oof. Another one destroyed by over-aggressive video compression. See the source code link for a better version: community.wolfram.com/groups/-

Caught

Voronoi diagram of stereographic projection of some spherical spirals.

Source code and slightly more explanation: community.wolfram.com/groups/- mathstodon.xyz/media/Emwp_r0Ru

Platonic II

Stereographic projection of the 5 Platonic solids

Platonic I

Stereographic projection of the 5 Platonic solids

Our paper on the least symmetric triangle has been published by Geometriae Dedicata: rdcu.be/GIkL

Here’s another fun image from the paper, which comes up in the course of determining the least symmetric acute triangle: mathstodon.xyz/media/3p4i0S_rV

Small Changes

Stereographic projection of a Hamiltonian cycle on the great rhombicosidodecahedron.

Source code and more explanation: community.wolfram.com/groups/- mathstodon.xyz/media/uh-1e9hg3

Throw

A Hamiltonian cycle on the vertices of the 120-cell.

Source code and more explanation: community.wolfram.com/groups/- mathstodon.xyz/media/Kzas7Me2P

How Does That Work?

Hamiltonian cycle on the 5-cell.

All Day

Stereographic projection of a Hamiltonian cycle on the 24-cell.

Touch ’Em All

A Hamiltonian cycle on the hypercube.

Source code and more explanation: community.wolfram.com/groups/- mathstodon.xyz/media/X3jJNFvol

Inside

Stereographic projection of points on the Clifford torus

Source code and more explanation: community.wolfram.com/groups/- mathstodon.xyz/media/H2IiI1zbI

Lean In

The equatorial 2-sphere in $S^3$, manipulated.

Fall Out

Mapping a rotating circle on the sphere to the plane. Here's the map: first, send (almost every) point on the sphere to the point on the $z=1$ plane contained in the same line through the origin. Then, invert the plane in the unit circle.

Allegory

A bunch of Brownian bridges approximating the unit circle.

(Not a GIF this time) mathstodon.xyz/media/QhHqmQQ8p

Microcosm

Stereographic projection of (part of) the cube grid.

Who’s the Boss?

Stereographic projection of a spherical pyramid.

Flat

Stereographic projection (followed by orthogonal projection to the plane) of a flat torus in the 3-sphere.

Take the square grid, inverse stereographic project to the sphere, then orthogonally project to the unit disk. Now, before mapping, translate the whole grid by $-t(1,2)$ as $t$ varies from $-1$ to $1$. This is the result.