Rhombicosacron

Rhombicosacron
File:DU56 rhombicosacron.png
Type	Star polyhedron
Face	File:DU56 facets.png
Elements	F = 60, E = 120 V = 50 (χ = −10)
Symmetry group	Ih, [5,3], *532
Index references	DU56
dual polyhedron	Rhombicosahedron

In geometry, the rhombicosacron (or midly dipteral ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform rhombicosahedron, U56. It has 50 vertices, 120 edges, and 60 crossed-quadrilateral faces.

Proportions

Each face has two angles of $\arccos (\frac{3}{4})\approx 41.40962210927^{\circ }$ and two angles of $\arccos (-\frac{1}{6})\approx 99.59406822686^{\circ }$. The diagonals of each antiparallelogram intersect at an angle of $\arccos (\frac{1}{8}+\frac{7\sqrt{5}}{24})\approx 38.99630966387^{\circ }$. The dihedral angle equals $\arccos (-\frac{5}{7})\approx 135.58469140281^{\circ }$. The ratio between the lengths of the long edges and the short ones equals $\frac{3}{2}+\frac{1}{2}\sqrt{5}$, which is the square of the golden ratio.

External links

• Uniform polyhedra and duals

Template:Asbox