Dodecagrammic crossedantiprism
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Wikipedia : http://en.wikipedia.org/wiki/Dodecagrammic_crossedantiprismDodecagrammic crossedantiprism  

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 
Schläfli symbol  s{2,24/7} 
Coxeter diagram 

Symmetry group  D_{12d} 
Dual polyhedron  Dodecagrammic concave deltohedron 
Properties  nonconvex 
In geometry, the dodecagrammic crossedantiprism 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.
See also
External links
Wikimedia Commons has media related to Antiprisms. 
 Weisstein, Eric W. "Antiprism". MathWorld.
 Paper models of prisms and antiprisms
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