Gyroelongated pentagonal birotunda

Gyroelongated pentagonal birotunda
Type Johnson
J47 - J48 - J49
Faces 4x10 triangles
2+10 pentagons
Edges 90
Vertices 40
Vertex configuration 2x10(3.5.3.5)
2.10(34.5)
Symmetry group D5
Dual polyhedron -
Properties convex, chiral
Net

In geometry, the gyroelongated pentagonal birotunda is one of the Johnson solids (J48). As the name suggests, it can be constructed by gyroelongating a pentagonal birotunda (either J34 or the icosidodecahedron) by inserting a decagonal antiprism between its two halves.

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 gyroelongated pentagonal birotunda is one of five Johnson solids which are chiral, meaning that they have a "left-handed" and a "right-handed" form. In the illustration to the right, each pentagonal face on the bottom half of the figure is connected by a path of two triangular faces to a pentagonal face above it and to the left. In the figure of opposite chirality (the mirror image of the illustrated figure), each bottom pentagon would be connected to a pentagonal face above it and to the right. The two chiral forms of J48 are not considered different Johnson solids.

See also

  • Weisstein, Eric W. "Johnson Solid". MathWorld.
    • Weisstein, Eric W. "Gyroelongated pentagonal birotunda". MathWorld.
  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 .
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