
This moving image of a projection of the four-dimensional 120-cell was made using Stella 4d, software you can try for free here: http://www.software3d.com/stella.php

This moving image of a projection of the four-dimensional 120-cell was made using Stella 4d, software you can try for free here: http://www.software3d.com/stella.php

In this polyhedron, there are, easily visible, twenty light blue faces which are equilateral triangles. Inside the polyhedron (and therefore harder to spot) are thirty purple faces which are Golden rectangles, along with twelve large, orange regular pentagonal faces.
To try the software I used to make this polyhedron, please visit www.software3d.com/stella.php.



It’s not the same one you can easily find in textbooks.
[Later edit] For a step-by-step explanation of this construction, see this post: https://robertlovespi.wordpress.com/2014/08/10/a-euclidean-construction-of-a-regular-pentagon-with-a-given-edge-length/.
