20a
Category 20a - Antiprisms
Above are sections of all 6 of the antiprisms: Gap is the famous grand antiprism, padiap is it's spiky conjugate, gudap is a double antiprism, the others are the Johnson Antiprisms.
The 4-D antiprisms are unusual polychora that are not actually traditional antiprisms, but are unusual types of antiprisms, they are as follows:
1117. Gap - the grand antiprism - this one is well known among 4-D geometers, and is mentioned in Coxeter's book Regular Complex Polytopes. Its verf resembles an ike with 2 adjacent corners completely cut off revealing 2 trapezoids surrounded by triangles. The cells are 20 paps (5 AP) which form 2 orthogonal rings of 10, and 300 tets - it has 100 vertices - it can be considered as a "super" pentagonal double antiprism. It was discovered by John Horton Conway and Richard Guy.
1118. Padiap - pentagrammatic double inverted antiprism - this is the stary conjugate of the grand antiprism. Its verf looks like a gike with parts removed and with two crossed trapezoids on it. Cells are 20 starps (5/3 AP) which form 2 orthogonal interpenitrating rings of 10, and 300 tets - it has 100 vertices - it can be considered as a super pentagrammatic double retroprism.
1119. Gudap - great duoantiprism - this is the only known duoantiprism that is uniform, there are other duoantiprisms, but they are not uniform (they are isogonal however). Gudap is actually the 5x5/3 duoantiprism. It has odd looking sections. The verf is a fusion of a wedge with a crossed wedge. Cells are 10 paps, 10 starps, and 100 tets - has 50 vertices.
1120. Sidtidap - small ditrigonary icosidodecahedral (sidtid) antiprism - this one and the next two are more like real antiprisms, these three were discovered by Norman Johnson - and are refered to as the Johnson Antiprisms. All three have 40 vertices. The verf of this one is a triangular cupola. Cells are 2 sidtids, 12 staps (5/2 AP), and 40 tets.
1121. Ditdidap - ditrigonary dodecadodecahedral (ditdid) antiprism - belongs to sidtidap regiment, verf is a faceting of the 3 cupola. Cells are 2 ditdids, 12 staps, and 12 paps.
1122. Gidtidap - great ditrigonary icosidodecahedral (gidtid) antiprism - belongs to sidtidap regiment, verf is a faceting of 3 cupola. Cells are 2 gidtids, 12 paps, and 40 tets. The verfs of the Johnson Antiprisms can be seen on George's Multidimensional Glossary under "Johnson Antiprisms".
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