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Great deltoidal icositetrahedron

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Great deltoidal icositetrahedron
Type Star polyhedron
Face
Elements F = 24, E = 48
V = 26 (χ = 2)
Symmetry group Oh, [4,3], *432
Index references DU17
dual polyhedron Nonconvex great rhombicuboctahedron

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.

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

Proportions

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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

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  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
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Weisstein, Eric W. "Great Deltoidal Icositetrahedron". MathWorld.