# Dodecagrammic crossed-antiprism

Dodecagrammic crossed-antiprism
Type Uniform polyhedron
Faces 2 {12}
24 {3}
Edges 48
Vertices 24
Vertex configuration 12/7.3.3.3
Wythoff symbol |2 2 12/7
Coxeter diagram
Symmetry group D12d
Dual polyhedron Dodecagrammic concave deltohedron
Properties nonconvex

In geometry, the dodecagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two dodecagrams.

Antiprisms are similar to prisms except the bases are twisted relative to each other, and that the side faces are triangles, rather than quadrilaterals. Crossed=antiprism have the triangles crossing the origin.

In the case of a uniform 12/5 base, one usually considers the case where its copy is offset by half'. 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 dodecagonal bases and, connecting those bases, 24 isosceles triangles.