| 词条 | Hemi-octahedron |
| 释义 |
|image=Hemi-octahedron2.png |type=abstract regular polyhedron globally projective polyhedron |schläfli={3,4}/2 or {3,4}3 |faces=4 triangles |edges=6 |vertices=3 |symmetry=S4, order 24 |vertex_config=3.3.3.3 |dual=hemicube |properties= non-orientable Euler characteristic 1 }} A hemi-octahedron is an abstract regular polyhedron, containing half the faces of a regular octahedron. It has 4 triangular faces, 6 edges, and 3 vertices. Its dual polyhedron is the hemicube. 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 can be seen as a square pyramid without its base. It can be represented symmetrically as a hexagonal or square Schlegel diagram: It has an unexpected property that there are two distinct edges between every pair of vertices – any two vertices define a digon. See also
References
External links
1 : Projective polyhedra |
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