Ionic diminished Coxeter group [[10,2+,10]] of order 400
Properties
convex
A net showing two disjoint rings of 10 antiprisms. 200 tetrahedra (yellow) are in face contact with the antiprisms and 100 tetrahedra (red) contact only other tetrahedra.
In geometry, the grand antiprism or pentagonal double antiprismoid is a uniform 4-polytope (4-dimensional uniform polytope) bounded by 320 cells: 20 pentagonal antiprisms, and 300 tetrahedra. It is an anomalous, non-Wythoffian uniform 4-polytope, discovered in 1965 by Conway and Guy.[1][2] Topologically, under its highest symmetry, the pentagonal antiprisms have D5d symmetry and there are two types of tetrahedra, one with S4 symmetry and one with Cs symmetry.
^J.H. Conway and M.J.T. Guy: Four-Dimensional Archimedean Polytopes, Proceedings of the Colloquium on Convexity at Copenhagen, page 38 und 39, 1965. (Michael Guy is son of Richard K. Guy)
to that of the 3-dimensional antiprisms. However, the grandantiprism is the only convex uniform analogue of the antiprism in 4 dimensions (although the...
In geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected...
prisms and antiprisms that contain pentagons or pentagrams as faces — the pentagonal prism and antiprism, and the pentagrammic prism, antiprism, and crossed-antiprism...
In geometry, the pentagonal antiprism is the third in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two...
120-cell, small stellated 120-cell, great icosahedral 120-cell, and great grand 120-cell. Muriel Pritchett, University of Georgia "To Span the Globe" Archived...
include the great dirhombicosidodecahedron in three dimensions and the grandantiprism in four dimensions. The terminology for the convex uniform polytopes...
excluding two infinite sets of prismatic forms. They discovered the grandantiprism in the process, the only non-Wythoffian uniform polychoron. Conway...
Pierre-Philippe (2021). "Clifford Spinors and Root System Induction: H4 and the GrandAntiprism". Advances in Applied Clifford Algebras. 31 (3). Springer Science and...
antiprismoid where n is an odd number greater than one, including the grandantiprism with pairs of trapezoid rather than square faces. Augmented sphenocorona...
Hein. Also with Conway, an enumeration led to the discovery of the grandantiprism, an unusual uniform polychoron in four dimensions. The two had met...
resulting figure is generally not uniform except for two cases: the grandantiprism and its conjugate, the pentagrammic double antiprismoid (with p = 5...
hexagonal antiprism with the same D5d, [2+,10] symmetry, order 20. The dodecagrammic antiprism, s{2,24/5} and dodecagrammic crossed-antiprism, s{2,24/7}...
building into eight tall isosceles triangles, or an elongated square antiprism. Near its middle, the tower forms a perfect octagon, and then culminates...
uniform star polyhedra including two infinite series, of prisms and of antiprisms, and their duals. The uniform and dual uniform star polyhedra are also...
30, 48, 60, 120 sides Trapezohedra, the duals of the infinite set of antiprisms, with kite faces: any even number not divisible by 4 (so that a face will...
have vertices corresponding to a prism ({n/m}#{} where n is odd) or an antiprism ({n/m}#{} where n is even). All polygons in 3 space have an even number...
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