page_title: Deltoidal icositetrahedron
section_title: Related polyhedra and tilings
hierarchical_section_title: Deltoidal icositetrahedron / Related polyhedra and tilings
caption_attribution_description: English: Spherical polyhedron en:deltoidal icositetrahedron
context_page_description: In geometry, a deltoidal icositetrahedron is a Catalan solid. Its dual polyhedron is the rhombicuboctahedron.
context_section_description: The deltoidal icositetrahedron  is one of a family of duals to the uniform polyhedra related to the cube and regular octahedron.
  When projected onto a sphere (see right), it can be seen that the edges make up the edges of an octahedron and cube arranged in their dual positions. It can also be seen that the threefold corners and the fourfold corners can be made to have the same distance to the center. In that case the resulting icositetrahedron will no longer have a rhombicuboctahedron for a dual, since for the rhombicuboctahedron the centers of its squares and its triangles are at different distances from the center.
  This polyhedron is topologically related as a part of sequence of deltoidal polyhedra with face figure (V3.4.n.4), and continues as tilings of the hyperbolic plane. These face-transitive figures have (*n32) reflectional symmetry.
caption: Spherical deltoidal icositetrahedron
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