# Decagonal antiprism

Uniform Decagonal antiprism Type Prismatic uniform polyhedron
Elements F = 22, E = 40
V = 20 (χ = 2)
Faces by sides 20{3}+2{10}
Schläfli symbol s{2,20}
sr{2,10}
Wythoff symbol | 2 2 10
Coxeter diagram           Symmetry group D10d, [2+,20], (2*10), order 40
Rotation group D10, [10,2]+, (10.2.2), order 20
References U77(h)
Dual Decagonal trapezohedron
Properties convex Vertex figure
3.3.3.10

In geometry, the decagonal antiprism is the eighth in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.

Antiprisms are similar to prisms except the bases are twisted relative to each other, and that the side faces are triangles, rather than quadrilaterals.

In the case of a regular 10-sided base, one usually considers the case where its copy is twisted by an angle 180°/n. Extra regularity is obtained by the line connecting the base centers being perpendicular to the base planes, making it a right antiprism. As faces, it has the two n-gonal bases and, connecting those bases, 2n isosceles triangles.

If faces are all regular, it is a semiregular polyhedron.