Rhombicosacron

Rhombicosacron
DU56 rhombicosacron.png
Type Star polyhedron
Face 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.

ProportionsEdit

Each face has two angles of   and two angles of  . The diagonals of each antiparallelogram intersect at an angle of  . The dihedral angle equals  . The ratio between the lengths of the long edges and the short ones equals  , which is the square of the golden ratio.

ReferencesEdit

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

External linksEdit