page_title: Pentagonal icositetrahedron
section_title: Related polyhedra and tilings
hierarchical_section_title: Pentagonal icositetrahedron / Related polyhedra and tilings
caption_attribution_description: English: Spherical en:pentagonal icositetrahedron
context_page_description: In geometry, a pentagonal icositetrahedron or pentagonal icosikaitetrahedron is a Catalan solid which is the dual of the snub cube. In crystallography it is also called a gyroid.
  It has two distinct forms, which are mirror images of each other.
context_section_description: This polyhedron is topologically related as a part of sequence of polyhedra and tilings of pentagons with face configurations (V3.3.3.3.n). (The sequence progresses into tilings the hyperbolic plane to any n.) These face-transitive figures have (n32) rotational symmetry.
  The pentagonal icositetrahedron  is second in a series of dual snub polyhedra and tilings with face configuration V3.3.4.3.n.
  The pentagonal icositetrahedron is one of a family of duals to the uniform polyhedra related to the cube and regular octahedron.
caption: Spherical pentagonal icositetrahedron
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