Thirty-Three Polyhedra with Icosidodecahedral Symmetry

Note:  icosidodecahedral symmetry, a term coined (as far as I know) by George Hart, means exactly the same thing as icosahedral symmetry. I simply use the term I like better. Also, a few of these, but not many, are chiral.

15 reg decagons 30 reg hex 120 trapsl

15x5 20x61 30x62 120x5 182 total

20x9 12x5 and 60x6 and 60x5 total 152

360 triangles

362 faces 12x10 20x18 30x10' 60x7 60x3 and 120 tiny triangles

480 triangular faces

542 faces incl 30x16 20x12 60x6 60x6' 12x5 60x7 120x5 and 120 timy triangles


The images directly above and below show the shape of the most symmetrical 240-carbon-atom fullerene.


chiral convex hull Convex hull

compound five tet

The image above is of the compound of five tetrahedra. This compound is chiral, and the next image is the compound of the compound above, and its mirror-image.

Compound of enantiomorphic pair

Comvnvex hjsdgaull

Conhgvedsfasdfx hull

Convedsfasdfx hull

Convex hjsdgaull

Convex hulfsgl

Convex hullll

Dual of Cjhfonvex hull

Dual of Convex hull

Dual of Convex hullb

dual of kite-variant of snub dodec

Faceted Convex hull augmentation with length 5 prisms

Faceted Convex hull

features twenty reg dodecagons 12 reg pents 60 kites 60 rectangles

In the next two, I was experimenting with placing really big spheres at the vertices of polyhedra. The first one is the great dodecahedron, rendered in this unusual style, with the faces rendered invisible.

great dodec


icosa variant

kites and triangles

rhombi and octagons

Stellated Poly



I made these using Stella 4d: Polyhedron Navigator. You may try this program for free at

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