Tetrated dodecahedron

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Tetrated dodecahedron
Tetrated dodecahedron.svg
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
TetratedDodeca flat.png
3D model of a tetrated dodecahedron Tetrated dodecahedron.stl
3D model of a tetrated dodecahedron
Model built with polydron Physical model of tetrated dodecahedron.png
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]

Contents

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.

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

(Johnson solid)
Dodecahedron.png Icosidodecahedron.png Pentagonal orthobirotunda solid.png
Dodecahedron flat.svg Icosidodecahedron flat.svg Johnson solid 34 net.png

See also

Notes

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