Small hexacronic icositetrahedron

In geometry, the small hexacronic icositetrahedron is the dual of the small cubicuboctahedron. It is visually identical to the small rhombihexacron. A part of each dart lies inside the solid, hence is invisible in solid models.

Small hexacronic icositetrahedron

Type	Star polyhedron
Face
Elements	F = 24, E = 48 V = 20 (χ = −4)
Symmetry group	O_h, [4,3], *432
Index references	DU₁₃
dual polyhedron	Small cubicuboctahedron

3D model of a small hexacronic icositetrahedron

Proportions

Its faces are darts, having two angles of $\arccos({\frac {1}{4}}+{\frac {1}{2}}{\sqrt {2}})\approx 16.842\,116\,236\,30^{\circ }$ , one of $\arccos({\frac {1}{2}}-{\frac {1}{4}}{\sqrt {2}})\approx 81.578\,941\,881\,85^{\circ }$ and one of $360^{\circ }-\arccos(-{\frac {1}{4}}-{\frac {1}{8}}{\sqrt {2}})\approx 244.736\,825\,645\,55^{\circ }$ . Its dihedral angles equal $\arccos({\frac {-7-4{\sqrt {2}}}{17}})\approx 138.117\,959\,055\,51^{\circ }$ . The ratio between the lengths of the long edges and the short ones equals $2-{\frac {1}{2}}{\sqrt {2}}\approx 1.292\,893\,218\,81$ .

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gollark: PwnCC *said* something about a zero-day, but I'm not entirely sure about that one since it was never demonstrated. I still don't recommend running it except on stuff you don't need much and can easily stick in a disk drive for formatting.

gollark: I meant "probably nobody bothered much".

gollark: Probably.

gollark: I do think it's at least resonably secure though.

References

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

External links

Eric W. Weisstein, Small hexacronic icositetrahedron (Uniform polyhedron) at MathWorld.

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