Gyroelongated pentagonal birotunda

Infobox_Polyhedron with net


Polyhedron_Type=Johnson
J₄₇ - J₄₈ - J₄₉
Face_List=4x10 triangles
2+10 pentagons
Edge_Count=90
Vertex_Count=40
Symmetry_Group=D₅
Vertex_List=2x10(3.5.3.5)
2.10(3⁴.5)
Dual=-
Property_List=convex, chiral
Net_

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In geometry, the gyroelongated pentagonal birotunda is one of the Johnson solids ("J"₄₈). As the name suggests, it can be constructed by gyroelongating a pentagonal birotunda (either "J"₃₄ or the icosidodecahedron) by inserting a decagonal antiprism between its two halves.

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 "J"₄₈ are not considered different Johnson solids.

The 92 Johnson solids were named and described by Norman Johnson in 1966.

External links

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** MathWorld | urlname=GyroelongatedPentagonalBirotunda | title=Gyroelongated pentagonal birotunda