Tetrated dodecahedron

Short description: Near-miss Johnson solid with 28 faces

Tetrated dodecahedron

Type| Near-miss Johnson solid
Faces| 4 equilateral triangles
12 isosceles triangles
12 pentagons
Edges| 54
Vertices| 28
Vertex configuration| 4 (5.5.5)
12 (3.5.3.5)
12 (3.3.5.5)
Symmetry group| Td
Properties| convex
Net
File:Tetrated dodecahedron.stl3D model of a tetrated dodecahedron Model built with polydron

In geometry, the tetrated dodecahedron is a near-miss Johnson solid. It was first discovered in 2002 by Alex Doskey. It was then independently rediscovered in 2003, and named, by Robert Austin.[1]

It has 28 faces: twelve regular pentagons arranged in four panels of three pentagons each, four equilateral triangles (shown in blue), and six pairs of isosceles triangles (shown in yellow). All edges of the tetrated dodecahedron have the same length, except for the shared bases of these isosceles triangles, which are approximately 1.07 times as long as the other edges. This polyhedron has tetrahedral symmetry.

Topologically, as a near-miss Johnson solid, the four triangles corresponding to the face planes of a tetrahedron are always equilateral, while the pentagons and the other triangles only have reflection symmetry.

## Related polyhedra

Dodecahedron
(Platonic solid)  | Icosidodecahedron
(Archimedean solid)  | Pentagonal
orthobirotunda
(Johnson solid)

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## See also

* Tetrahedrally diminished dodecahedron

## Notes

1. ↑ Tetrated dodecahedra

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Near-miss Johnson solids

Truncated forms|

* Truncated triakis tetrahedron
* Chamfered cube (Truncated rhombic dodecahedron)
* Chamfered dodecahedron (Truncated rhombic triacontahedron)

Other forms|

* Tetrated dodecahedron
* Rectified truncated icosahedron
* Pentahexagonal pyritoheptacontatetrahedron

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