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| Elongated square gyrobicupola | |
|---|---|
| Type | Johnson |
| Faces | 8 triangles 18 squares |
| Edges | 48 |
| Vertices | 24 |
| Vertex configuration | 3.43 |
| Symmetry group | D4d |
| Dual polyhedron | - |
| Properties | convex, locally vertex-regular |
In geometry, the Elongated square gyrobicupola is one of the
Johnson solids (J37).It is unique amongst the Johnson solids in being locally vertex-regular - the arrangement of the 4 faces incident on any vertex is the same for all vertices. However, it is not vertex-regular, and consequently not one of the Archimedean solids, as the
group of symmetries of the solid do not act transitively on the vertices. Basically, two types of vertices can be distinguished by their "neighbours of neighbours".It can be constructed by twisting one of the square cupolae on a rhombicuboctahedron by 45 degrees. Its similarity to the rhombicuboctahedron gives it the alternative name pseudorhombicuboctahedron.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
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