Jump to content

Great hexagonal hexecontahedron

From Wikipedia, the free encyclopedia

This is the current revision of this page, as edited by 1234qwer1234qwer4 (talk | contribs) at 22:29, 27 December 2022 (Importing Wikidata short description: Polyhedron with 60 faces (shortdescs-in-category)). The present address (URL) is a permanent link to this version.

(diff) ← Previous revision | Latest revision (diff) | Newer revision → (diff)
Great hexagonal hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 180
V = 104 (χ = −16)
Symmetry group I, [5,3]+, 532
Index references DU64
dual polyhedron Great snub dodecicosidodecahedron
3D model of a great hexagonal hexecontahedron

In geometry, the great hexagonal hexecontahedron (or great astroid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great snub dodecicosidodecahedron. It is partially degenerate, having coincident vertices, as its dual has coplanar pentagrammic faces.

Proportions[edit]

The faces are nonconvex hexagons. Denoting the golden ratio by , the hexagons have one angle of , one of , and four angles of . They have two long edges, two of medium length and two short ones. If the long edges have length , the medium ones have length and the short ones . The dihedral angle equals .

References[edit]

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

External links[edit]