Sphenoid
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| Sphenoid | |
|---|---|
 | |
| Rank | 3 |
| Notation | |
| Coxeter diagram | oox&#x |
| Elements | |
| Faces | 1+1 isosceles triangles, 2 scalene triangles |
| Edges | 1+1+2+2 |
| Vertices | 1+1+2 |
| Vertex figure | 1+1 isosceles triangles, 2 scalene triangles |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Army | Sphenoid |
| Regiment | Sphenoid |
| Dual | Sphenoid |
| Conjugate | Sphenoid |
| Abstract & topological properties | |
| Flag count | 24 |
| Euler characteristic | 2 |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | A1×I×I, order 2 |
| Flag orbits | 12 |
| Convex | Yes |
| Nature | Tame |
A sphenoid is a type of tetrahedron with only one symmetry axis. As such it has two different isosceles triangles and two identical scalene triangles as faces, and can also be called a mirror-symmetric tetrahedron.
In vertex figures[edit | edit source]
Sphenoids occur as vertex figures in a total of 23 non-prismatic uniform polychora, including all the cantitruncated polychora, also known as great rhombates. They also appear as vertex figures in the prisms of the 10 3D truncates.