Gyroelongated triangular bicupola
| Gyroelongated triangular bicupola | |
|---|---|
| Type | Johnson J43 - J44 - J45 |
| Faces | 2+3.6 triangles 6 squares |
| Edges | 42 |
| Vertices | 18 |
| Vertex configuration | 6(3.4.3.4) 2.6(34.4) |
| Symmetry group | D3 |
| Dual polyhedron | - |
| Properties | convex, chiral |
| Net | |
In geometry, the gyroelongated triangular bicupola is one of the Johnson solids (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.
Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[1]
References
- ^ Stephen Wolfram, "Gyroelongated triangular bicupola" from Wolfram Alpha. Retrieved July 30, 2010.