A339349 The number of n-faced polyhedra formed when a cuboctahedron is internally cut by all the planes defined by any three of its vertices.

2304, 3000, 944, 408, 48, 24

Offset

4,1

Comments

For a cuboctahedron create all possible internal planes defined by connecting any three of its vertices. Use all the resulting planes to cut the polyhedron into individual smaller polyhedra. The sequence lists the number of resulting n-faced polyhedra, where 4 <= n <= 9.

See A339348 for the corresponding sequence for the rhombic dodecahedron, the dual polyhedron of the cuboctahedron.

Links

Table of n, a(n) for n=4..9.

Hyung Taek Ahn and Mikhail Shashkov, Geometric Algorithms for 3D Interface Reconstruction.

Scott R. Shannon, Image showing the 67 internal plane cuts on the external edges and faces.

Scott R. Shannon, Image of the 2304 4-faced polyhedra.

Scott R. Shannon, Image of the 3000 5-faced polyhedra.

Scott R. Shannon, Image of the 944 6-faced polyhedra.

Scott R. Shannon, Image of the 408 7-faced polyhedra.

Scott R. Shannon, Image of the 48 8-faced polyhedra. None of these are visible on the surface of the cuboctahedron.

Scott R. Shannon, Image of the 24 9-faced polyhedra. None of these are visible on the surface of the cuboctahedron.

Scott R. Shannon, Image of all 6728 polyhedra. The colors are the same as those used in the above images.

Eric Weisstein's World of Mathematics, Cuboctahedron.

Wikipedia, Cuboctahedron.

Example

The cuboctahedron has 12 vertices, 14 faces, and 24 edges. It is cut by 67 internal planes defined by any three of its vertices, resulting in the creation of 6728 polyhedra. No polyhedra with ten or more faces are created.

Crossrefs

Cf. A339348, A338622, A338801, A338808, A338825.

Sequence in context: A270854 A260292 A359321 * A281927 A179699 A195652

Adjacent sequences: A339346 A339347 A339348 * A339350 A339351 A339352

Keyword

nonn,fini,full

Author

Scott R. Shannon, Dec 01 2020

Status

approved