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Deltoidal icositetrahedron
Type	Catalan
Face polygon	kite
Faces	24
Edges	48
Vertices	26 = 6 + 8 + 12
Face configuration	V3.4.4.4
Symmetry group	octahedral (Oh)
Dual polyhedron	rhombicuboctahedron
Properties	convex, face-uniform

A deltoidal icositetrahedron (or trapezoidal icositetrahedron) is a Catalan solid which looks a bit like an overinflated cube. Its dual polyhedron is the rhombicuboctahedron.

The 24 faces are deltoids or geometric kites, not trapezoids; the trapezohedron is similarly misnamed.

The trapezoidal icositetrahedron is a crystal habit often formed by the mineral analcime and occasionally garnet. The shape is often called a trapezohedron in mineral contexts, although in solid geometry that name refers to completely different class of polyhedron. The Shining Trapezohedron of the fictional Lovecraft Mythos was probably intended to refer to a crystal of this shape.

See also

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• Deltohedron

Catalan solids

icositetraedro deltoidal | 凧形二十四面体 | Icositetraedro deltoidal