The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part Two

Just like I did in the first part of this two-part post, I’m starting with the snub dodecahedron’s 43rd stellation.

43rd stellation Snub Dodeca

This time, though, this polyhedral exploration is going in another direction. In the image below, the yellow kites seen above are shown augmented with prisms. The height of the prisms is equal to the average edge length of those kites.

Augmented Stellated Snub Dodeca

Creating the convex hull of this augmented polyhedron is the next step.

Cool polyhedron before TTMFR

The program I’m using to make these changes to polyhedra is called Stella 4d (it’s available here). The next step is using a function of Stella called “try to make faces regular.” The result is shown below.

242 faces 20 hex and 12 penta and 2x60 quads of two types and 30 quads of a third type and 60 triangles

Finally, I’m adjusting the coloring scheme so hexagons, pentagon, and triangles each get their own color, with a fourth color used for all three types of quadrilateral.

cool polyhedron colored by number of sides per face

Because I like this result, I’m stopping here.

The 43rd Stellation of the Snub Dodecahedron, and Related Polyhedra, Part One

If you stellate the snub dodecahedron 43 times, this is the result. The yellow faces are kites, not rhombi.

Stellated Snub Dodeca refl

Like the snub dodecahedron itself, this polyhedron is chiral. Here is the mirror-image of the polyhedron shown above.

Stellated Snub Dodeca 43rd mirror image

Any chiral polyhedron may be combined with its own mirror-image to create a compound.

Compound of enantiomorphic pair x

This is the dual of the snub dodecahedron’s 43rd stellation.

Stellated Snub Dodeca refl chiral dual

This dual is also chiral. Here is its reflection.

43rd stellation snub dodeca dual reflection

Finally, here is the compound of both duals.

Compound of enantiomorphic pair duals

I used Stella 4d: Polyhedron Navigator to create these images. You may try this program for yourself at http://www.software3d.com/Stella.php.