Gyroelongated square bipyramid

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Gyroelongated square bipyramid
Gyroelongated square dipyramid.png
TypeJohnson
J16 - J17 - J18
Faces2×8 triangles
Edges24
Vertices10
Vertex configuration2(34)
8(35)
Symmetry groupD4d, [2+,8], (2*4)
Rotation groupD4, [2,4]+, (422)
Dual polyhedronTruncated square trapezohedron
Propertiesconvex, deltahedron
Net
Johnson solid 17 net.png

In geometry, the gyroelongated square bipyramid or heccaidecadeltahedron is one of the Johnson solids (J17). As the name suggests, it can be constructed by gyroelongating an octahedron (square bipyramid) by inserting a square antiprism between its congruent halves. It is one of the eight strictly-convex deltahedra.

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1]

The dual of the gyroelongated square bipyramid is a square truncated trapezohedron with 10 faces: 8 pentagons and 2 square.

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  1. ^ Johnson, Norman W. (1966), "Convex polyhedra with regular faces", Canadian Journal of Mathematics, 18: 169–200, doi:10.4153/cjm-1966-021-8, MR 0185507, Zbl 0132.14603.