Snub Cube

My new favourite geometry discovery this week is the Snub Cube. It comes in two 'flavours' (chiralities) that are mirror-images of each other.

But how to build a 3D model? Wikipedia to the rescue (or so I thought)!

The description of the vertex sets (one set for each chirality) states: "Cartesian coordinates for the vertices of a snub cube are all the even permutations of (±1, ±1/t, ±t) with an even number of plus signs, along with all the odd permutations with an odd number of plus signs, where t ≈ 1.83929 is the tribonacci constant. Taking the even permutations with an odd number of plus signs, and the odd permutations with an even number of plus signs, gives a different snub cube, the mirror image."

This is followed by another set of calculations to down-scale the coordinates so generated to an object with a unit edge length.

Ten-out-of-ten for conciseness! But zero-out-of-ten for usefulness when it comes to building your own vertex sets (OK, maybe one-out-of-ten).

So, I wanted to document the vertex sets more explicitly (unit edge length, to 5d.p.), in case it helps other Amateur Geometry Explorers out there. I also dropped both vertex sets into an OpenSCAD file (edge length = 10, to 4d.p.): snubcube.scad.

Chirality A

(0.62123, 0.33775, -1.14261)
(0.62123, -0.33775, 1.14261)
(-0.62123, 0.33775, 1.14261)
(-0.62123, -0.33775, -1.14261)
(0.33775, 1.14261, -0.62123)
(0.33775, -1.14261, 0.62123)
(-0.33775, 1.14261, 0.62123)
(-0.33775, -1.14261, -0.62123)
(1.14261, 0.62123, -0.33775)
(1.14261, -0.62123, 0.33775)
(-1.14261, 0.62123, 0.33775)
(-1.14261, -0.62123, -0.33775)
(0.62123, 1.14261, 0.33775)
(0.62123, -1.14261, -0.33775)
(-0.62123, -1.14261, 0.33775)
(-0.62123, 1.14261, -0.33775)
(0.33775, 0.62123, 1.14261)
(0.33775, -0.62123, -1.14261)
(-0.33775, -0.62123, 1.14261)
(-0.33775, 0.62123, -1.14261)
(1.14261, 0.33775, 0.62123)
(1.14261, -0.33775, -0.62123)
(-1.14261, -0.33775, 0.62123)
(-1.14261, 0.33775, -0.62123)

Chirality B

(0.62123, 1.14261, -0.33775)
(0.62123, -1.14261, 0.33775)
(-0.62123, 1.14261, 0.33775)
(-0.62123, -1.14261, -0.33775)
(0.33775, 0.62123, -1.14261)
(0.33775, -0.62123, 1.14261)
(-0.33775, 0.62123, 1.14261)
(-0.33775, -0.62123, -1.14261)
(1.14261, 0.33775, -0.62123)
(1.14261, -0.33775, 0.62123)
(-1.14261, 0.33775, 0.62123)
(-1.14261, -0.33775, -0.62123)
(0.62123, 0.33775, 1.14261)
(0.62123, -0.33775, -1.14261)
(-0.62123, -0.33775, 1.14261)
(-0.62123, 0.33775, -1.14261)
(0.33775, 1.14261, 0.62123)
(0.33775, -1.14261, -0.62123)
(-0.33775, -1.14261, 0.62123)
(-0.33775, 1.14261, -0.62123)
(1.14261, 0.62123, 0.33775)
(1.14261, -0.62123, -0.33775)
(-1.14261, -0.62123, 0.33775)
(-1.14261, 0.62123, -0.33775)

What!? You want more decimal places!? How about 15d.p.?: 1.142613508925962; 0.621226410556585; 0.337753973813752 (you'll have to do you own "±" management).

All Snub Cube assets by Chris Molloy are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

SNUB CUBE

Chirality A

Chirality B