Some Stellations of the Truncated Dodecahedron

The stellation-series of the truncated dodecahedron contains some interesting polyhedra. Selections from this series appear below.

24th Stellated Trunc Dodeca chiral

The polyhedron above is the 24th stellation of the truncated dodecahedron, while the one below is the 25th stellation.

25th stellation of Trunc Dodeca

27th Stellated Trunc Dodeca chiral

The polyhedron immediately above is the truncated dodecahedron’s 27th stellation. The one shown below is the 29th stellation.

29th Stellated Trunc Dodeca chiral

36th Stellated Trunc Dodeca chiral

The last two polyhedra in this post are the truncated dodecahedron’s 36th stellation (above), and its 70th stellation (below).

70th Stellated Trunc Dodeca

These images were created using Stella 4d, software available here.


The 11th, 13th, and 15th Stellations of the Icosahedron

First, this is the 11th stellation.

Stellated Icosa the 11th

Next, the 13th:

13th Stellated Icosa

And, finally, the 15th stellation of the icosahedron:

15th Stellated Icosa

I used Stella 4d, which you can find here, to make these.

Two Different Cluster-Polyhedra

Augmented Icosa with RIDs

An icosahedron is hidden from view in the center of this cluster-polyhedron. To create the cluster, each of the icosahedron’s triangles was augmented with a rhombicosidodecahedron. The resulting cluster has the overall shape of a dodecahedron.

To create the next cluster-polyhedron, I started with the one above, and then augmented each of its triangular faces with icosidodecahedra. 

large cluster os icosidodecahedrons.gif

I used a program named Stella 4d: Polyhedron Navigator to create these cluster-polyhedra. This software may be bought (or tried for free) at this website

An Expansion of the Rhombic Enneacontahedron with 422 Faces, Together with Its 360-Faced Dual

422 faces expansion of the REC

The polyhedron above had 422 faces and 360 vertices. In dual polyhedra, these numbers are reversed, so the next polyhedra (the dual of the first one) has 360 faces and 422 vertices. Both were created using Stella 4d, available here.

422 faces expansion of the REC the dual with 360 faces