page_title: Triakis tetrahedron
section_title: Related polyhedra
hierarchical_section_title: Triakis tetrahedron / Related polyhedra
caption_attribution_description: English: Spherical polyhedron en:triakis tetrahedron
context_page_description: In geometry, a triakis tetrahedron is a Catalan solid with 12 faces. Each Catalan solid is the dual of an Archimedean solid. The dual of the triakis tetrahedron is the truncated tetrahedron.
  The triakis tetrahedron can be seen as a tetrahedron with a triangular pyramid added to each face; that is, it is the Kleetope of the tetrahedron. It is very similar to the net for the 5-cell, as the net for a tetrahedron is a triangle with other triangles added to each edge, the net for the 5-cell a tetrahedron with pyramids attached to each face. This interpretation is expressed in the name.
  The length of the shorter edges is that of the longer edges. If the triakis tetrahedron has shorter edge length 1, it has area √11 and volume √2.
context_section_description: The triakis tetrahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane. These face-transitive figures have (*n32) reflectional symmetry.
caption: Spherical triakis tetrahedron
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