Gyrobifastigium
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 quarter-turn to one prism. It is the only Johnson solid that can tile three-dimensional space.
| 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 | Elongated tetragonal disphenoid |
| Properties | convex, honeycomb |
| Net | |
It is also the vertex figure of the nonuniform p-q duoantiprism (if p and q are greater than 2). Despite the fact that p, q = 3 would yield a geometrically identical equivalent to the Johnson solid, it lacks a circumscribed sphere that touches all vertices, except for the case p = 5, q = 5/3, which represents a uniform great duoantiprism.
Its dual, the elongated tetragonal disphenoid, can be found as cells of the duals of the p-q duoantiprisms.
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