A Dodecahedron with Four Symetrically-Truncated Vertices

dodeca with 4 verts truncated tet symm

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.]

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. The majority of these things 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.
This entry was posted in Mathematics and tagged , , , , , , , , . Bookmark the permalink.

4 Responses to A Dodecahedron with Four Symetrically-Truncated Vertices

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

    Like

  2. Tom R says:

    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

    Liked by 1 person

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s