Small rhombihexacron

Small rhombihexacron

Type	Star polyhedron
Face
Elements	F = 24, E = 48 V = 18 (χ = −6)
Symmetry group	O_h, [4,3], *432
Index references	DU₁₈
dual polyhedron	Small rhombihexahedron

In geometry, the small rhombihexacron (or small dipteral disdodecahedron) is the dual of the small rhombihexahedron. It is visually identical to the small hexacronic icositetrahedron. Its faces are antiparallelograms formed by pairs of coplanar triangles.

Proportions

Each antiparallelogram has two angles of $\arccos({\frac {1}{4}}+{\frac {1}{2}}{\sqrt {2}})\approx 16.842\,116\,236\,30^{\circ }$ and two angles of $\arccos(-{\frac {1}{2}}+{\frac {1}{4}}{\sqrt {2}})\approx 98.421\,058\,118\,15^{\circ }$ . The diagonals of each antiparallelogram intersect at an angle of $\arccos({\frac {1}{4}}+{\frac {1}{8}}{\sqrt {2}})\approx 64.736\,825\,645\,55^{\circ }$ . The dihedral angle equals $\arccos({\frac {-7-4{\sqrt {2}}}{17}})\approx 138.117\,959\,055\,51^{\circ }$ . The ratio between the lengths of the long edges and the short ones equals ${\sqrt {2}}$ .

References

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

External links

Weisstein, Eric W. "Small rhombihexacron". MathWorld.