Gyrobifastigium
| Gyrobifastigium | |
|---|---|
 |
|
| Type | Johnson J25 - J26 - J27 |
| Faces | 4 triangles 4 squares |
| Edges | 14 |
| Vertices | 8 |
| Vertex configuration | 4(3.42) 4(3.4.3.4) |
| Symmetry group | D2d |
| Dual polyhedron | - |
| Properties | convex, honeycomb |
| Net | |
 |
|
In geometry, the gyrobifastigium is the 26th Johnson solid (J26). It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a half-turn to one prism.
The name comes from the Latin fastigium, meaning a sloping roof.[1] In the standard naming convention of the Johnson solids, bi- means two solids connected at their bases, and gyro- means the two halves are twisted with respect to each other.
The gyrobifastigium's place in the list of Johnson solids, immediately before the bicupolas, is explained by viewing it as a digonal gyrobicupola. Just as the other regular cupolas have an alternating sequence of squares and triangles surrounding a single polygon at the top (triangle, square or pentagon), each half of the gyrobifastigium consists of just alternating squares and triangles, connected at the top only by a ridge.
The gyrobifastigium is one of five convex polyhedra with regular faces capable of space-filling (the others being the cube, truncated octahedron, triangular and hexagonal prism) and it is the only Johnson solid capable of doing so.[2][3][4] The 92 Johnson solids were named and described by Norman Johnson in 1966.
[edit] Formulae
The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[5]
[edit] Dual polyhedron
The dual of the gyrobifastigium has 8 faces: 4 isoceles triangles, and 4 parallelograms.
| Dual gyrobifastigium |
|---|
 |
[edit] References
- ^ William Smith, D.C.L., LL.D.: A Dictionary of Greek and Roman Antiquities, John Murray, London, 1875
- ^ Weisstein, Eric W., "Space-Filling Polyhedron" from MathWorld.
- ^ Weisstein, Eric W., "Johnson solid" from MathWorld.
- ^ Weisstein, Eric W., "Gyrobifastigium" from MathWorld.
- ^ Stephen Wolfram, "Gyrobifastigium" from Wolfram Alpha. Retrieved July 21, 2010.
