page_title: Trapezohedron
section_title: Forms
hierarchical_section_title: Trapezohedron / Forms
caption_attribution_description: English: Gyroelongated triangular bipyramid with colplanar triangular faces
context_page_description: The n-gonal trapezohedron, antidipyramid, antibipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism. With a highest symmetry, its 2n faces are congruent kites. The faces are symmetrically staggered.
  The n-gon part of the name does not reference the faces here but arrangement of vertices around an axis of symmetry. The dual n-gonal antiprism has two actual n-gon faces.
  An n-gonal trapezohedron can be dissected into two equal n-gonal pyramids and an n-gonal antiprism.
context_section_description: A n-trapezohedron has 2n quadrilateral faces, with 2n+2 vertices. Two vertices are on the polar axis, and the others are in two regular n-gonal rings of vertices.
  Special cases:
  n=2: A degenerate form, form a geometric tetrahedron with 6 vertices, 8 edges, and 4 degenerate kite faces that are degenerated into triangles. Its dual is a degenerate form of antiprism, also a tetrahedron.
  n=3: In the case of the dual of a triangular antiprism the kites are rhombi (or squares), hence these trapezohedra are also zonohedra. They are called rhombohedra. They are cubes scaled in the direction of a body diagonal. Also they are the parallelepipeds with congruent rhombic faces.
  A special case of a rhombohedron is one in which the rhombi which form the faces have angles of 60° and 120°. It can be decomposed into two equal regular tetrahedra and a regular octahedron. Since parallelepipeds can fill space, so can a combination of regular tetrahedra and regular octahedra.
caption: A 60° rhombohedron, dissected into a central regular octahedron and two regular tetrahedra
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