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A Few of My Favorite Spaces: The Bicylinder by Evelyn Lamb

A Few of My Favorite Spaces: The Bicylinder

Also known as mouhefanggai or the Steinmetz solid, this shape appeared in the first Chinese explorations of the volume of a sphere… 6 more words

Geometry

Counting uniforms

Euclid’s “proof” that there are exactly five regular (convex) polyhedra is well known and pretty simple. Observe that there have to be at least three faces meeting at each vertex, and the angles of those faces have to add up to less than 360°. 1,153 more words

Geometry

Forty-seven more

Turns out you can do the same thing with 47 icosahedrons. The rhombic dodecahedron is clearer here.

Geometry

Forty-seven

Here’s a nice one, from Stewart’s Chapter VII ‘Exploration of (R)(A) toroids’. Take an octahedron and attach a pair of octahedrons to each face:(That’s 17 octahedra, one in the center and two in each of the eight arms.) That makes something roughly cube shaped. 69 more words

Geometry

Folder full of holes

So I now have created all of the examples from Chapter V, ‘Simplest (R)(A)(Q)(T) toroids of genus p=1’, in Antiprism, and they’re in this Google Drive folder… 47 more words

Geometry