Sesquitruncated cuboctahedron
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| Sesquitruncated cuboctahedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Near-miss |
| Elements | |
| Faces | 48 scalene triangles, 12 rhombi, 8 triangular-symmetric enneagons, 6 dodecagons |
| Edges | 24+48+48+48 |
| Vertices | 24+24+48 |
| Vertex figures | 48 scalene triangles |
| 24 isosceles trapezoids | |
| 24 isosceles trapezoids | |
| Measures (edge length 1) | |
| Edge length ratio | 1.01407 |
| Central density | 1 |
| Number of external pieces | 74 |
| Related polytopes | |
| Conjugate | None |
| Abstract & topological properties | |
| Euler characteristic | 2 |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | B3, order 48 |
| Convex | Yes |
| Nature | Tame |
The Sesquitruncated cuboctahedron is a near-miss Johnson solid. Its faces are 48 scalene triangles, 12 rhombi, 8 enneagons and 6 dodecagons.
To construct it, one needs to inscribe an enneagon in every triangle and a dodecagon in every square of cuboctahedron then fill all the remaining gaps with scalene triangles and rhombi.
Although this solid is locally Euclidean since it has 3.4.3.12 vertices, it is still notable for having an edge length ratio close to 1.
The sesquitruncated cuboctahedron is the largest cell of the sesquitruncated rectified cubic honeycomb which is a near-miss CRF honeycomb.
Its other cell types are: sesquitruncated octahedra, deformed cuboctahedra and deformed tetrahedra.
