Antiprism

Set of uniform $n$ -gonal antiprisms
Set of uniform n-gonal antiprisms
	Uniform hexagonal antiprism (n = 6)
Type	uniform in the sense of semiregular polyhedron
Faces	2 regular n-gons; 2n equilateral triangles
Edges	4n
Vertices	2n
Vertex configuration	3.3.3.n
Schläfli symbol	{ }⊗{n} ; s{2,2n}; sr{2,n}
Conway notation	An
Coxeter diagram	;
Symmetry group	Dnd, [2+,2n], (2*n), order 4n
Rotation group	Dn, [2,n]+, (22n), order 2n
Dual polyhedron	convex dual-uniform n-gonal trapezohedron
Properties	convex, vertex-transitive, regular polygon faces, congruent & coaxial bases
Net
	Net of uniform enneagonal antiprism (n = 9)

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 by an alternating band of $2 n$ triangles. They are represented by the Conway notation $A n$ .

Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron.

Antiprisms are similar to prisms, except that the bases are twisted relatively to each other, and that the side faces (connecting the bases) are $2 n$ triangles, rather than $n$ quadrilaterals.

The dual polyhedron of an $n$ -gonal antiprism is an $n$ -gonal trapezohedron.

^ N.W. Johnson: Geometries and Transformations, (2018) ISBN 978-1-107-10340-5 Chapter 11: Finite symmetry groups, 11.3 Pyramids, Prisms, and Antiprisms, Figure 11.3c

[1] N.W. Johnson: Geometries and Transformations, (2018) ISBN 978-1-107-10340-5 Chapter 11: Finite symmetry groups, 11.3 Pyramids, Prisms, and Antiprisms, Figure 11.3c

[1]

Set of uniform $n$ -gonal antiprisms
Uniform hexagonal antiprism ( $n = 6$ )
Type	uniform in the sense of semiregular polyhedron
Faces	2 regular $n$ -gons $2 n$ equilateral triangles
Edges	$4 n$
Vertices	$2 n$
Vertex configuration	$3.3.3. n$
Schläfli symbol	${ }\otimes{n}$ ^[1] $s{2,2 n} sr{2, n}$
Conway notation	$A n$
Coxeter diagram
Symmetry group	$D n d, [2 +,2 n], (2* n)$ , order $4 n$
Rotation group	$D n, [2, n] +, (22 n)$ , order $2 n$
Dual polyhedron	convex dual-uniform $n$ -gonal trapezohedron
Properties	convex, vertex-transitive, regular polygon faces, congruent & coaxial bases
Net

Net of uniform enneagonal antiprism ( $n = 9$ )