Truncated square antiprism

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Truncated square antiprism
Truncated square antiprism.png
TypeTruncated antiprism
Schläfli symbol ts{2,8}
tsr{4,2} or
Conway notation tA4
Faces18: 2 {8}, 8 {6}, 8 {4}
Edges48
Vertices32
Symmetry group D4d, [2+,8], (2*4), order 16
Rotation group D4, [2,4]+, (224), order 8
Dual polyhedron
Propertiesconvex, 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.

Contents

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. [1]

Gyroelongated triamond square bicupola.png
Truncated antiprisms
SymmetryD2d, [2+,4], (2*2)D3d, [2+,6], (2*3)D4d, [2+,8], (2*4)D5d, [2+,10], (2*5)
Antiprisms Digonal antiprism.png
s{2,4}
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 4.pngCDel node.png
(v:4; e:8; f:6)
Trigonal antiprism.png
s{2,6}
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 6.pngCDel node.png
(v:6; e:12; f:8)
Square antiprism.png
s{2,8}
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 8.pngCDel node.png
(v:8; e:16; f:10)
Pentagonal antiprism.png
s{2,10}
CDel node h.pngCDel 2x.pngCDel node h.pngCDel 10.pngCDel node.png
(v:10; e:20; f:12)
Truncated
antiprisms
Truncated digonal antiprism.png
ts{2,4}
(v:16;e:24;f:10)
Truncated octahedron prismatic symmetry.png
ts{2,6}
(v:24; e:36; f:14)
Truncated square antiprism.png
ts{2,8}
(v:32; e:48; f:18)
Truncated pentagonal antiprism.png
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.

Snub square antiprism colored.png

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References