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• This has conventionally been thought of as the first discovery of these shapes, but they may have been known earlier: an unsigned printing block for the net of a hexagonal antiprism has been attributed to Hieronymus Andreae, who died in 1556.
• In geometry, the regular icosahedron (or simply icosahedron) is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with regular faces to each of its pentagonal faces, or by putting points onto the cube.
• The equilateral triangle can be found in various tilings, and in polyhedrons such as the deltahedron and antiprism.
• Of all vertex-transitive polyhedra that are not prisms or antiprisms, it has the largest sum of angles (90 + 120 + 144 = 354 degrees) at each vertex; only a prism or antiprism with more than 60 sides would have a larger sum.
• A regular skew polygon in 3-space can be seen as nonplanar paths zig-zagging between two parallel planes, defined as the side-edges of a uniform antiprism.
• Pentagonal antiprism, Decagonal prism, Pentagonal cupola, Snub disphenoid, Elongated square dipyramid, Metabidiminished icosahedron, Hexagonal bipyramid, Hexagonal trapezohedron, Triakis tetrahedron, Rhombic dodecahedron, Hendecagonal pyramid, Trapezo-rhombic dodecahedron, Rhombo-hexagonal dodecahedron.
• Examples of polyhedrons are the pentakis dodecahedron is constructed from the dodecahedron by attaching the base of pentagonal pyramids onto each pentagonal face, small stellated dodecahedron is constructed from a regular dodecahedron stellated by pentagonal pyramids, and regular icosahedron constructed from a pentagonal antiprism by attaching two pentagonal pyramids onto its pentagonal bases.
• In geometry, the gyroelongated square bicupola is the Johnson solid constructed by attaching two square cupolae on each base of octagonal antiprism.
• In geometry, the snub square antiprism is the Johnson solid that can be constructed by snubbing the square antiprism.
• The sphenocorona is also the vertex figure of the isogonal n-gonal double antiprismoid where n is an odd number greater than one, including the grand antiprism with pairs of trapezoid rather than square faces.
• It is one of the three common shapes for transition metal complexes with eight vertices other than the chemical structure other than square antiprism and the snub disphenoid.
• Two rings of ten pentagonal antiprisms each bound the hypersurface of the four-dimensional grand antiprism.
• Pentagonal trapezohedron (5-trapezohedron, antiprism dual) often used as a die in role playing games, known as a d10.
• The runcinated order-5 cubic honeycomb or runcinated order-4 dodecahedral honeycomb , has cube, dodecahedron, and pentagonal prism cells, with an irregular triangular antiprism vertex figure.
• 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.
• In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
• There are also 41 convex semiregular 4-polytope, including the non-Wythoffian grand antiprism and the snub 24-cell.
• A facetting of a trigonal trapezohedron creates a compound of two right triangular pyramids with a triangular antiprism core.
• In geometry, the heptagonal antiprism is the fifth in an infinite set of antiprisms formed by two parallel polygons separated by a strip of triangles.
• In 4-dimensional geometry, a uniform antiprismatic prism or antiduoprism is a uniform 4-polytope with two uniform antiprism cells in two parallel 3-space hyperplanes, connected by uniform prisms cells between pairs of faces.

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