Tetrated dodecahedron

Tetrated dodecahedron
Typenear-miss Johnson solid
Faces4+12 triangles
12 pentagons
Edges54
Vertices28
Vertex configuration4 (5.5.5)
12 (3.5.3.5)
12 (3.3.5.5)
Symmetry groupTd
Propertiesconvex

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.

Net

The 12 pentagons and 16 triangles are colored in this net by their locations within the tetrahedral symmetry.

Related polyhedra

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

(Johnson solid)

See also

Notes

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