Medial rhombic triacontahedron

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Medial rhombic triacontahedron
DU36 medial rhombic triacontahedron.png
Type Star polyhedron
Face DU36 facets.png
Elements F = 30, E = 60
V = 24 (χ = −6)
Symmetry group Ih, [5,3], *532
Index references DU36
dual polyhedron Dodecadodecahedron

In geometry, the medial rhombic triacontahedron is a nonconvex isohedral polyhedron. It is the dual of the dodecadodecahedron. It has 30 intersecting rhombic faces.

It can also be called the small stellated triacontahedron.

Stellation[edit]

The Medial rhombic triacontahedron is a stellation of the rhombic triacontahedron. The convex hull of the dodecadodecahedron is an icosidodecahedron.

Related hyperbolic tiling[edit]

It is topologically equivalent to a quotient space of the hyperbolic order-5 square tiling, by distorting the rhombi into squares. As such, it is topologically a regular polyhedron of index two:[1]

Uniform tiling 45-t0.png

Note that the order-5 square tiling is dual to the order-4 pentagonal tiling, and a quotient space of the order-4 pentagonal tiling is topologically equivalent to the dual of the medial rhombic triacontahedron, the dodecadodecahedron.

See also[edit]

References[edit]

  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

External links[edit]