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.

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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.

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