Gyroelongated square bicupola
Encyclopedia
In geometry
, the gyroelongated square bicupola is one of the Johnson solid
s (J45). As the name suggests, it can be constructed by gyroelongating a square bicupola (J28
or J29
) by inserting an octagonal antiprism
between its congruent halves.
The gyroelongated square 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 left half of the figure is connected by a path of two triangular faces to a square face below it and to the right. 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 to the right. The two chiral forms of J45 are not considered different Johnson solids.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the gyroelongated square bicupola is one of the Johnson solid
Johnson solid
In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. There is no requirement that each face must be the same polygon, or that the same polygons join around...
s (J45). As the name suggests, it can be constructed by gyroelongating a square bicupola (J28
Square orthobicupola
In geometry, the square orthobicupola is one of the Johnson solids . As the name suggests, it can be constructed by joining two square cupolae along their octagonal bases, matching like faces...
or J29
Square gyrobicupola
In geometry, the square gyrobicupola is one of the Johnson solids . Like the square orthobicupola , it can be obtained by joining two square cupolae along their bases...
) by inserting an octagonal antiprism
Antiprism
In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles...
between its congruent halves.
The gyroelongated square bicupola is one of five Johnson solids which are chiral
Chirality (mathematics)
In geometry, a figure is chiral if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. For example, a right shoe is different from a left shoe, and clockwise is different from counterclockwise.A chiral object...
, meaning that they have a "left-handed" and a "right-handed" form. In the illustration to the right, 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 to the right. 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 to the right. The two chiral forms of J45 are not considered different Johnson solids.
The 92 Johnson solids were named and described by Norman Johnson in 1966.