Truncated square antiprismTypeTruncated antiprismSchläfli symbolts{2,8}tsr{4,2} or Conway notationtA4Faces18: 2 {8}, 8 {6}, 8 {4} Edges48Vertices32Symmetry groupD4d, [2+,8], (2*4), order 16Rotation groupD4, [2,4]+, (224), order 8Dual polyhedronPropertiesconvex, zonohedron The truncated square antiprism one in an infinite series of truncated antiprisms, constructed as a truncated square antiprism. It has 18 faces, 2 octagons, 8 hexagons, and 8 squares.
Gyroelongated triamond square bicupola If the hexagons are folded, it can be constructed by regular polygons. Or each folded hexagon can be replaced by two triamonds, adding 8 edges (56), and 4 faces (32). This form is called a gyroelongated triamond square bicupola.Convex Triamond Regular Polyhedra
Related polyhedra
+ Truncated antiprismsSymmetryD2d, [2+,4], (2*2)D3d, [2+,6], (2*3)D4d, [2+,8], (2*4)D5d, [2+,10], (2*5)Antiprismss{2,4}(v:4; e:8; f:6)s{2,6}(v:6; e:12; f:8)s{2,8}(v:8; e:16; f:10)s{2,10}(v:10; e:20; f:12)Truncatedantiprismsts{2,4}(v:16;e:24;f:10)ts{2,6}(v:24; e:36; f:14)ts{2,8}(v:32; e:48; f:18)ts{2,10}(v:40; e:60; f:22)
Snub square antiprism Although it can't be made by all regular planar faces, its alternation is the Johnson solid, the snub square antiprism.
References
Snub Anti-Prisms