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Tetrated dodecahedron

Near-miss Johnson solid with 28 faces

Field	Value
image	Tetrated Dodecahedron.gif
type	Near-miss Johnson solid
faces	4 equilateral triangles
12 isosceles triangles
12 pentagons
edges	54
vertices	28
vertex_config	4 (5.5.5)12 (3.5.3.5)12 (3.3.5.5)
symmetry	Td
properties	convex
net	TetratedDodeca flat.png

12 isosceles triangles 12 pentagons

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.

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)	Pentagonalorthobirotunda(Johnson solid)
[[File:Dodecahedron.png	120px]]	[[File:Icosidodecahedron.png	120px]]	[[File:Pentagonal orthobirotunda solid.png	120px]]
[[File:Dodecahedron flat.svg	120px]]	[[File:Icosidodecahedron flat.svg	120px]]	[[File:Johnson solid 34 net.png	120px]]

Notes

References

[http://www.orchidpalms.com/polyhedra/acrohedra/nearmiss/Tetrated%20Dodecahedra.html Tetrated dodecahedra]

Info: Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

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