Great Triambic Icosahedron

The great triambic icosahedron is the dual of the great ditrigonal icosidodecahedron and Wenninger model whose appearance is the same as the medial triambic icosahedron (the dual of the ditrigonal dodecadodecahedron), since internal vertices are hidden from view (Wenninger 1983, p. 42). The medial triambic icosahedron has hidden pentagrammic faces, while the great triambic icosahedron has hidden triangular faces (Wenninger 1983, pp. 45 and 47-50).

The convex hull of the great ditrigonal icosidodecahedron is a regular dodecahedron, whose dual is the icosahedron, so the dual of the great ditrigonal icosidodecahedron (the great triambic icosahedron) is one of the icosahedron stellations (Wenninger 1983, p. 42). In fact, the medial triambic icosahedron corresponds to icosahedron stellation , which is stellation number 30 in the enumeration of Coxeter et al. (1999, pp. 47 and 64).

References

Coxeter, H. S. M.; Du Val, P.; Flather, H. T.; and Petrie, J. F. The Fifty-Nine Icosahedra. Stradbroke, England: Tarquin Publications, 1999.

Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, pp. 41 and 46, 1983.

Wenninger, M. J. "Ninth Stellation of the Icosahedron." §34 in Polyhedron Models. New York: Cambridge University Press, p. 55, 1989.

See also