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 kites, not trapezoids; the trapezohedron is similarly misnamed. The short and long edges of each kite are in the ratio 1.00:1.29.
The deltoidal icositetrahedron is topologically identical to a cube which has all of its edges bisected:
Occurances in nature and culture
The deltoidal 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 a particular class of polyhedron
The Shining Trapezohedron of the fictional Lovecraft Mythos was probably intended to refer to a crystal of this shape.
- Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)