Gyroelongated pentagonal cupolarotunda
Encyclopedia
In geometry
, the gyroelongated pentagonal cupolarotunda is one of the Johnson solid
s (J47). As the name suggests, it can be constructed by gyroelongating a pentagonal cupolarotunda (J32
or J33
) by inserting a decagon
al antiprism
between its two halves.
The gyroelongated pentagonal cupolarotunda 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 square 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 square face above it and to the right. The two chiral forms of J47 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 pentagonal cupolarotunda 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 (J47). As the name suggests, it can be constructed by gyroelongating a pentagonal cupolarotunda (J32
Pentagonal orthocupolarotunda
In geometry, the pentagonal orthocupolarotunda is one of the Johnson solids . As the name suggests, it can be constructed by joining a pentagonal cupola and a pentagonal rotunda along their decagonal bases, matching the pentagonal faces...
or J33
Pentagonal gyrocupolarotunda
In geometry, the pentagonal gyrocupolarotunda is one of the Johnson solids . Like the pentagonal orthocupolarotunda , it can be constructed by joining a pentagonal cupola and a pentagonal rotunda along their decagonal bases...
) by inserting a decagon
Decagon
In geometry, a decagon is any polygon with ten sides and ten angles, and usually refers to a regular decagon, having all sides of equal length and each internal angle equal to 144°...
al 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 two halves.
The gyroelongated pentagonal cupolarotunda 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 pentagonal 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 left. In the figure of opposite chirality (the mirror image of the illustrated figure), each bottom pentagon would be connected to a square face above it and to the right. The two chiral forms of J47 are not considered different Johnson solids.
The 92 Johnson solids were named and described by Norman Johnson in 1966.