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Set of trapezohedra
Decagonal trapezohedron
Faces2n kites
Face configurationV3.3.3.n
Symmetry groupDnd
Dual polyhedronantiprism
Propertiesconvex, face-transitive

The n-gonal trapezohedron, antidipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism. Its 2n faces are congruent deltoids (or kites). The faces are symmetrically staggered.

The name trapezohedron can be misleading as the faces are not trapezoids, but the alternative deltohedron is sometimes confused with the unrelated term deltahedron. It is quite possible, but not necessarily true, that the name trapezohedron could be derived from trapezium (a quadrilateral with no parallel sides) as opposed to trapezoid, since the faces are kites, a type of trapezium.



In texts describing the crystal habits of minerals, the word trapezohedron is often used to refer to the polyhedron properly known as a deltoidal icositetrahedron.


Trigonal trapezohedron Tetragonal trapezohedron Pentagonal trapezohedron Hexagonal trapezohedron Octagonal trapezohedron Decagonal trapezohedron

    • A cube is a special case trigonal trapezohedron with square faces
  2. Tetragonal trapezohedron - 8 kite faces - dual square antiprism
  3. Pentagonal trapezohedron - 10 kite faces - dual pentagonal antiprism
  4. Hexagonal trapezohedron - 12 kite faces - dual hexagonal antiprism
  5. Heptagonal trapezohedron - 14 kite faces - dual heptagonal antiprism
  6. Octagonal trapezohedron - 16 kite faces - dual octagonal antiprism
  7. Enneagonal trapezohedron - 18 kite faces - dual enneagonal antiprism
  8. Decagonal trapezohedron - 20 kite faces - dual decagonal antiprism







In Popular Culture

See also

External links

nl:Trapezoëderno:Trapesohedron pt:Trapezoedro

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