Gyroelongated pentagonal bicupola
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In geometry, the gyroelongated pentagonal bicupola is one of the Johnson solids (J46Script error: No such module "Check for unknown parameters".). As the name suggests, it can be constructed by gyroelongating a pentagonal bicupola (J30Script error: No such module "Check for unknown parameters". or J31Script error: No such module "Check for unknown parameters".) by inserting a decagonal antiprism between its congruent halves.
The gyroelongated pentagonal bicupola 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 square face on the bottom half of the figure is connected by a path of two triangular faces to a square face above it and to the right. In the figure of opposite chirality (the mirror image of the illustrated figure), each bottom square would be connected to a square face above it and to the left. The two chiral forms of J46Script error: No such module "Check for unknown parameters". are not considered different Johnson solids.
Area and volume
With edge length a, the surface area is
and the volume is
References
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