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|Type||abstract regular polyhedron
globally projective polyhedron
|Symmetry group||S4, order 24|
Euler characteristic 1
It can be seen as an square pyramid without its base. It can be realized as a projective polyhedron (a tessellation of the real projective plane by 4 triangles), which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected and dividing the hemisphere into four equal parts.
It has an unexpected property that there are two distinct edges between every pair of vertices – any two vertices define a digon.
- McMullen, Peter; Schulte, Egon (December 2002), "6C. Projective Regular Polytopes", Abstract Regular Polytopes (1st ed.), Cambridge University Press, pp. 162–165, ISBN 0-521-81496-0
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