Deltoidal icositetrahedron

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Deltoidal icositetrahedron
Click on picture for large version. Click here for spinning version.
Type	Catalan
Face polygon	kite
Faces	24
Edges	48
Vertices	26 = 6 + 8 + 12
Face configuration	V3.4.4.4
Symmetry group	octahedral (O_h)
Dihedral angle	138° 6' 34"
Dual polyhedron	rhombicuboctahedron
Properties	convex, face-transitive
Net

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 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 a particular class of polyhedron.

The Shining Trapezohedron of the fictional Lovecraft Mythos was probably intended to refer to a crystal of this shape.

[edit] See also

Deltoidal hexecontahedron

From Wikipedia's entry for H.P. Lovecraft's "The Haunter of the Dark":

The Shining Trapezohedron is a window on all space and time. Described as a "crazily angled stone", it is unlikely to be a true trapezohedron because of the Old Ones' penchant for bizarre non-Euclidean angles. It was created on dark Yuggoth and brought to Earth by the Old Ones, where it was placed in its box aeons before the first human beings appeared. It has further history in Atlantis and with the Pharaohs of Egypt, until it was finally unearthed and brought to New England.

[edit] References

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)