Great deltoidal icositetrahedron

In geometry, the great deltoidal icositetrahedron (or great sagittal disdodecahedron) is the dual of the nonconvex great rhombicuboctahedron. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models.

Great deltoidal icositetrahedron
TypeStar polyhedron
Face
ElementsF = 24, E = 48
V = 26 (χ = 2)
Symmetry groupOh, [4,3], *432
Index referencesDU17
dual polyhedronNonconvex great rhombicuboctahedron

One of its halves can be rotated by 45 degrees to form the pseudo great deltoidal icositetrahedron, analogous to the pseudo-deltoidal icositetrahedron.

Proportions

Faces have three angles of and one of . Its dihedral angles equal . The ratio between the lengths of the long edges and the short ones equals .

References

  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208

Weisstein, Eric W. "Great Deltoidal Icositetrahedron". MathWorld.

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