Tetrahedrally expanded tetrated dodecahedron
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| Tetrahedrally expanded tetrated dodecahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Near-miss |
| Elements | |
| Faces | 12 isosceles triangles, 4+4 regular triangles, 6 rectangles, 12 isosceles trapezoids and 12 mirror-symmetric pentagons |
| Edges | 12+12+12+12+24+24 |
| Vertices | 12+12+24 |
| Vertex figures | 12+12 isosceles trapezoids |
| 12 irregular quadrilaterals | |
| Measures (based on regular pentagons of edge length 1) | |
| Edge length ratio | 1.03853 (Can be reduced to 1 if irregular pentagons are allowed) |
| Central density | 1 |
| Number of external pieces | 50 |
| Related polytopes | |
| Conjugate | None |
| Abstract & topological properties | |
| Euler characteristic | 2 |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | A3, order 24 |
| Convex | Yes |
| Nature | Tame |
The tetrahedrally expanded tetrated dodecahedron is a near-miss Johnson solid. Its faces are 12 isosceles triangles, 4+4 regular triangles, 6 rectangles, 12 isosceles trapezoids and 12 mirror-symmetric pentagons. It is one of the near-miss Johnson solids that has a version with only one edge length.
