A339528 The number of n-faced polyhedra formed when an elongated dodecahedron is internally cut by all the planes defined by any three of its vertices.

153736, 177144, 106984, 44312, 12120, 2464, 304, 24, 0, 8

Offset

4,1

Comments

For an elongated dodecahedron 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 <= 13.

Links

Table of n, a(n) for n=4..13.

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

Scott R. Shannon, Image showing the 268 internal plane cuts on the external edges and faces

Scott R. Shannon, Image showing the 153736 4-faced polyhedra.

Scott R. Shannon, Image showing the 153736 4-faced polyhedra, viewed from above.

Scott R. Shannon, Image showing the 12120 8-faced polyhedra, viewed from above.

Scott R. Shannon, Image showing the 2464 9-faced polyhedra, viewed from above.

Scott R. Shannon, Image of all 497096 polyhedra. The polyhedra are colored red,orange,yellow,green,blue,indigo,violet for face counts 4 to 10 respectively. The polyhedra with face counts 11 and 13 are not visible on the surface.

Eric Weisstein's World of Mathematics, Elongated Dodecahedron.

Wikipedia, Elongated dodecahedron.

Example

The elongated dodecahedron has 18 vertices, 28 edges and 12 faces (8 rhombi and 4 hexagons). It is cut by 268 internal planes defined by any three of its vertices, resulting in the creation of 497096 polyhedra. No polyhedra with 12 faces or 14 or more faces are created.

Crossrefs

Cf. A339348, A339349, A338622, A338801, A338808, A338825.

Sequence in context: A172732 A172789 A248594 * A234553 A073086 A341212

Adjacent sequences: A339525 A339526 A339527 * A339529 A339530 A339531

Keyword

nonn,fini,full

Author

Scott R. Shannon, Dec 08 2020

Status

approved