Two Convex Polyhedra with Tetrahedral Symmetry, Each Featuring Four Regular Dodecagons

tet variant featuring reg dodecagons and equits

The polyhedron above is a tetrahedrally-symmetric polyhedron featuring regular dodecagons and triangles, as well as two types of trapezoidal faces.

tet variant using reg dodecagons and hexagons

To make this second polyhedron from the first one, I first augmented each dodecagonal face with an antiprism, took the convex hull of the result, and then used the “try to make faces regular” function of the polyhedron-manipulation software I use, Stella 4d, which can be tried for free right here. The result is a polyhedron which maintains tetrahedral symmetry, and has, as faces, regular dodecagons and hexagons, as well as trapezoids and rectangles.

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