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Great pentakis dodecahedron

From Wikipedia, the free encyclopedia
Great pentakis dodecahedron
Type Star polyhedron
Face
Elements F = 60, E = 90
V = 24 (χ = −6)
Symmetry group Ih, [5,3], *532
Index references DU58
dual polyhedron Small stellated truncated dodecahedron
3D model of a great pentakis dodecahedron

In geometry, the great pentakis dodecahedron is a nonconvex isohedral polyhedron.

It is the dual of the uniform small stellated truncated dodecahedron. The pentagonal faces pass close to the center in the uniform polyhedron, causing this dual to be very spikey. It has 60 intersecting isosceles triangle faces. Part of each triangle lies within the solid, hence is invisible in solid models.

Proportions

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The triangles have one very acute angle of and two of . The dihedral angle equals .

References

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