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Truncated square antiprism

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Truncated square antiprism
Type Truncated antiprism
Schläfli symbol ts{2,8}
tsr{4,2} or
Conway notation tA4
Faces 18: 2 {8}, 8 {6}, 8 {4}
Edges 48
Vertices 32
Symmetry group D4d, [2+,8], (2*4), order 16
Rotation group D4, [2,4]+, (224), order 8
Dual polyhedron
Properties convex, 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

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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.[1]

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Truncated antiprisms
Symmetry D2d, [2+,4], (2*2) D3d, [2+,6], (2*3) D4d, [2+,8], (2*4) D5d, [2+,10], (2*5)
Antiprisms
s{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)
Truncated
antiprisms

ts{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

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Although it can't be made by all regular planar faces, its alternation is the Johnson solid, the snub square antiprism.

References

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