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|Bowers style acronym||Sladid|
|Vertex figure||8 triangles, 6+12 squares|
|Measures (edge length 1)|
|Conjugate||Great deltoidal icositetrahedron|
|Symmetry||B3, order 48|
The deltoidal icositetrahedron, also called the strombic icositetrahedron or small lanceal disdodecahedron, is one of the 13 Catalan solids. It has 24 kites as faces, with 6+12 order-4 and 8 order-3 vertices. It is the dual of the uniform small rhombicuboctahedron.
It can also be obtained as the convex hull of a cube, an octahedron, and a cuboctahedron. If the cube has unit edge length, the octahedron's edge length is and the cuboctahedron's edge length is
Each face of this polyhedron is a kite with its longer edges times the length of its shorter edges. These kites have three angles measuring and one angle measuring .
Vertex coordinates[edit | edit source]
A deltoidal icositetrahedron with dual edge length 1 has vertex coordinates given by all permutations of:
External links[edit | edit source]
- Klitzing, Richard. "Sladid".
- Wikipedia Contributors. "Deltoidal icositetrahedron".
- McCooey, David. "Deltoidal Icositetrahedron"