In geometry, the gyroelongated square bicupola is the Johnson solid constructed by attaching two square cupolae on each base of octagonal antiprism. It has the property of chirality.
Gyroelongated square bicupola | |
---|---|
Type | Johnson J44 – J45 – J46 |
Faces | 24 triangles 10 squares |
Edges | 56 |
Vertices | 24 |
Vertex configuration | |
Symmetry group | |
Properties | convex, chiral |
Net | |
The gyroelongated square bicupola is constructed by attaching two square cupolae on each base of octagonal antiprism, a process known as gyroelongation. This construction involves the removal of octagons, and replacing them with cupolae.[1] As a result, this polyhedron has twenty triangular and ten square faces.[2] The Johnson solid is the convex polyhedron with all of its faces are regular, and the gyroelongated square bicupola is one of them, enumerated as .[3]
Given that the edge length , the surface area is:
The gyroelongated square bicupola is one of five Johnson solids, which is chiral, meaning that they have a "left-handed" and a "right-handed" form. In the following illustration, each square face on the left half of the figure is connected by a path of two triangular faces to a square face below it and on the left. In the figure of opposite chirality (the mirror image of the illustrated figure), each square on the left would be connected to a square face above it and on the right. These two chiral forms are not considered different Johnson solids.[citation needed] It has the symmetry of dihedral group .[4]