Gyroelongated triangular bicupola
Encyclopedia
In geometry
, the gyroelongated triangular bicupola is one of the Johnson solid
s (J44). As the name suggests, it can be constructed by gyroelongating a triangular bicupola (either J27
or the cuboctahedron
) by inserting a hexagonal antiprism
between its congruent halves.
The gyroelongated triangular 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 J44 are not considered different Johnson solids.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
e for volume
and surface area
can be used if all faces are regular
, with edge length a:
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 triangular 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 (J44). As the name suggests, it can be constructed by gyroelongating a triangular bicupola (either J27
Triangular orthobicupola
In geometry, the triangular orthobicupola is one of the Johnson solids . As the name suggests, it can be constructed by attaching two triangular cupolas along their bases...
or the cuboctahedron
Cuboctahedron
In geometry, a cuboctahedron is a polyhedron with eight triangular faces and six square faces. A cuboctahedron has 12 identical vertices, with two triangles and two squares meeting at each, and 24 identical edges, each separating a triangle from a square. As such it is a quasiregular polyhedron,...
) by inserting a hexagonal antiprism
Hexagonal antiprism
In geometry, the hexagonal antiprism is the 4th in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps.If faces are all regular, it is a semiregular polyhedron.- See also :* Set of antiprisms...
between its congruent halves.
The gyroelongated triangular 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 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 J44 are not considered different Johnson solids.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
Formulae
The following formulaFormula
In mathematics, a formula is an entity constructed using the symbols and formation rules of a given logical language....
e for volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
and surface area
Surface area
Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra the surface area is the sum of the areas of its faces...
can be used if all faces are regular
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
, with edge length a: