Modifying a Snub Cube

This is the snub cube. It’s one of the thirteen Archimedean solids.

The first modification I made to this polyhedron was to stellate it once.

The next step was to augment each yellow face with a tall prism.

Next, I formed the convex hull of the above solid.

The software I use to manipulate polyhedra, Stella 4d, has a function called “try to make faces regular.” The last step of this short polyhedral journey was to use this function on the above convex hull.

If you would like to try Stella 4d for yourself, there is a free trial download available at

An Expanded Version of the Snub Cube

prism-expanded snub cube convex hull after TTMFR

To make this polyhedron, I started with a snub cube. Next, I augmented all triangular faces of it with prisms, then took the convex hull of the result. Finally, I used Stella 4d‘s “try to make faces regular” function on the convex hull.

Stella 4d: Polyhedron Navigator has a free trial download available here.

The Compound of Five Cubes, Augmented with Thirty Snub Cubes: Three Versions

Cubes 5 augmented by 30 snub cubes

This cluster-polyhedron was made with Stella 4d, software you can try at this website. Above, it is colored by face-type, referring to each face’s position within the overall cluster. In the image below, the original compound of five cubes contained one cube each, of five colors, and then each snub cube “inherited” its color from the cube to which it was attached.

Cubes 5

In the next version, the colors are chosen by the number of sides of each face.

Cubes 5

An Attempt to Blend Five Snub Cubes with One Snub Dodecahedron


Viewers will be the judges of how successful this attempt to blend these polyhedra actually is. I made it using Stella 4d, software you can try right here.

One Faceting, Each, of the Snub Cube and Snub Dodecahedron

Faceted snub cube

These are facetings of the snub cube (above) and snub dodecahedron (below). I made both using Stella 4d, software you can try for yourself right here.

faceted Snub Dodeca

Compounds of Enantiamorphic Archimedean Solid Duals

An enantiomorphic-pair compound requires a chiral polyhedron, for it is a compound of a polyhedron and its mirror image. Among the Archimedeans, only the snub cube and snub dodecahedron are chiral. For this reason, only threir duals are chiral, among the Archimedean duals, also known as the Catalan solids.

Compound of enantiomorphic pair snub cube duals

That’s a compound of two mirror-image snub cube duals (pentagonal icositetrahedra) above; the similar compound for the snub dodecahedron duals (pentagonal hexacontahedra) is below.

Compound of enantiomorphic pair

Both these compounds were made with Stella 4d, which is available at

A Polyhedral Journey, Beginning with the Snub Cube / Pentagonal Isositetrahedron Base/Dual Compound

The snub cube and its dual make an attractive compound. Since the snub cube is chiral, its chirality is preserved in this compound.

Penta Icositetra & snub cube compound

If you examine the convex hull of this compound, you will find it to be chiral as well.

Convex hull of snub cube& dual compound

Here is the mirror image of that convex hull:

Convex hull mirror image

These two convex hulls, of course, have twin, chiral, duals:

dual of Convex hull of snub cube& dual compound

Dual of Convex hull mirror image

The two chiral convex hulls above (the red, blue, and yellow ones), made an interesting compound, as well.

Compound of enantiomorphic pair not dual

This is also true of their chiral duals:

Compound of enantiomorphic pair

I next stellated this last figure numerous times (I stopped counting at ~200), to obtain this polyhedron:

Stellated Compound of enantiomorphic pair dual

After seeing this, I wanted to know what its dual would look like — and it was a nice polyhedron on which to end this particular polyhedral journey.

dual of Stellated Compound of enantiomorphic pair dual

I  make these transformations of polyhedra, and create these virtual models, using a program called Stella 4d. It may be purchased, or tried for free, at

An Excavated Snub Cube, with Two of Its “Cousins”


An Excavated Snub Cube

In this variation of the snub cube, twenty of the triangular faces have been excavated with short triangular pyramids. Since the snub cube is chiral, it’s possible to make a compound out of it and its mirror-image:

Compound of enantiomorphic pair of excavated snub cubes

A polyhedron which is somewhat similar to the first one shown here can be produced by faceting a snub cube:

Faceted Snub Cube

Stella 4d was used to create these images. You can find this program at