Deltoidal icositetrahedron
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| Deltoidal icositetrahedron | |
|---|---|
 Click on picture for large version. Click here for spinning version. |
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| Type | Catalan |
| Face polygon | kite |
| Faces | 24 |
| Edges | 48 |
| Vertices | 26 = 6 + 8 + 12 |
| Face configuration | V3.4.4.4 |
| Symmetry group | octahedral (Oh) or *432 |
| Dihedral angle | 138° 6' 34" |
| Dual polyhedron | rhombicuboctahedron |
| Properties | convex, face-transitive |
 Net |
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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.
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[edit] Related polyhedra
The deltoidal icositetrahedron is topologically identical to a cube which has all of its edges bisected:
[edit] Occurrences 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.
[edit] See also
- Deltoidal hexecontahedron
- The Haunter of the Dark H.P. Lovecraft's book includes this figure in the plot.
[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)
[edit] External links
- Eric W. Weisstein, Deltoidal icositetrahedron (Catalan solid) at MathWorld.
- Deltoidal (Trapezoidal) Icositetrahedron -- Interactive Polyhedron model
