Dodecahedra have icosahedral (also called icosidodecahedral) symmetry. In the figure above, this symmetry is changed to tetrahedral, by truncation of four vertices with positions corresponding to the vertices (or, instead, faces) of a tetrahedron. The interchangeability of vertices and faces for the tetrahedron is related to the fact that the tetrahedron is self-dual.

[Image created using *Stella 4d*, available here.]

### Like this:

Like Loading...

*Related*

## About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet.
The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.

(For some reason, I don’t see the image in the WP Reader…)

LikeLike

But I do see it when I visit your site.

LikeLiked by 1 person

This polyhedron is related to the self-dual “tetrahedrally diminished dodecahedron” where the truncation completely removes the original edges, and reduces the pentagons into trapezoids.

https://en.wikipedia.org/wiki/Tetrahedrally_diminished_dodecahedron

LikeLiked by 1 person

Tom, do you know if anyone has compiled a list of known polyhedra which are self-dual?

LikeLike