Small stellapentakis dodecahedron

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Small stellapentakis dodecahedron
TypeStar polyhedron
Face
ElementsF = 60, E = 90
V = 24 (χ = −6)
Symmetry groupIh, [5,3], *532
Index referencesDU37
dual polyhedronTruncated great dodecahedron

In geometry, the small stellapentakis dodecahedron is a nonconvex isohedral polyhedron. It is the dual of the truncated great dodecahedron. It has 60 intersecting triangular faces.

3D model of a small stellapentakis dodecahedron

Proportions

The triangles have two acute angles of arccos ⁡ ( 1 2 + 1 5 5 ) ≈ 18.699 407 085 149 ∘ {\displaystyle \arccos({\frac {1}{2}}+{\frac {1}{5}}{\sqrt {5}})\approx 18.699\,407\,085\,149^{\circ }} {\displaystyle \arccos({\frac {1}{2}}+{\frac {1}{5}}{\sqrt {5}})\approx 18.699\,407\,085\,149^{\circ }} and one obtuse angle of arccos ⁡ ( 1 10 − 2 5 5 ) ≈ 142.601 185 829 70 ∘ {\displaystyle \arccos({\frac {1}{10}}-{\frac {2}{5}}{\sqrt {5}})\approx 142.601\,185\,829\,70^{\circ }} {\displaystyle \arccos({\frac {1}{10}}-{\frac {2}{5}}{\sqrt {5}})\approx 142.601\,185\,829\,70^{\circ }}. The dihedral angle equals arccos ⁡ ( − 24 − 5 5 41 ) ≈ 149.099 125 827 35 ∘ {\displaystyle \arccos({\frac {-24-5{\sqrt {5}}}{41}})\approx 149.099\,125\,827\,35^{\circ }} {\displaystyle \arccos({\frac {-24-5{\sqrt {5}}}{41}})\approx 149.099\,125\,827\,35^{\circ }}. Part of each triangle lies within the solid, hence is invisible in solid models.

References