| Johnson solid (450 words) |
 | An example of a Johnson solid that is neither a platonic solid nor an archimedean solid is a square based pyramid; it has one square face and four triangular faces. |
| To have vertices, there must be at least three of the faces meeting at a point, and the total of their angles must be less than 360 degrees; i.e the corners of the face must be less than 120 degrees. |
| An octahedron would be a square bipyramid, a cuboctahedron would be a triangular gyrobicupola, and an icosidodecahedron would be a pentagonal gyrobirotunda. |
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