page_title: Rhombic triacontahedron
section_title: Stellations
hierarchical_section_title: Rhombic triacontahedron / Stellations
caption_attribution_description: English: en:Rhombic hexecontahedron
context_page_description: In geometry, the rhombic triacontahedron, sometimes simply called the triacontahedron as it is the most common thirty-faced polyhedron, is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. It is a Catalan solid, and the dual polyhedron of the icosidodecahedron. It is a zonohedron.
  The ratio of the long diagonal to the short diagonal of each face is exactly equal to the golden ratio, φ, so that the acute angles on each face measure 2 tan⁻¹ = tan⁻¹, or approximately 63.43°. A rhombus so obtained is called a golden rhombus.
  Being the dual of an Archimedean solid, the rhombic triacontahedron is face-transitive, meaning the symmetry group of the solid acts transitively on the set of faces. This means that for any two faces, A and B, there is a rotation or reflection of the solid that leaves it occupying the same region of space while moving face A to face B.
  The rhombic triacontahedron is somewhat special in being one of the nine edge-transitive convex polyhedra, the others being the five Platonic solids, the cuboctahedron, the icosidodecahedron, and the rhombic dodecahedron.
context_section_description: The rhombic triacontahedron has 227 fully supported stellations. 
  Another stellation of the Rhombic triacontahedron is the compound of five octahedra. 
  The total number of stellations of the rhombic triacontahedron is 358,833,097.
caption: Rhombic hexecontahedron
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