A339468 The number of n-faced polyhedra formed when a truncated tetrahedron is internally cut by all the planes defined by any three of its vertices.
4818, 4596, 2454, 816, 246, 60, 0, 0, 9
Offset: 4
Examples
The truncated tetrahedron has 12 vertices, 18 edges and 4 faces (4 equilateral triangles and 4 hexagons). It is cut by 82 internal planes defined by any three of its vertices, resulting in the creation of 12999 polyhedra. No polyhedra with 10, 11, or 13 or more faces are created.
Links
- Hyung Taek Ahn and Mikhail Shashkov, Geometric Algorithms for 3D Interface Reconstruction.
- Scott R. Shannon, Image showing the 82 internal plane cuts on the external edges and faces.
- Scott R. Shannon, Image of the 4818 4-faced polyhedra.
- Scott R. Shannon, Image of the 4596 5-faced polyhedra.
- Scott R. Shannon, Image of the 2454 6-faced polyhedra.
- Scott R. Shannon, Image of the 816 7-faced polyhedra.
- Scott R. Shannon, Image of the 246 8-faced polyhedra. None of these are visible on the surface.
- Scott R. Shannon, Image of the 60 9-faced polyhedra. None of these are visible on the surface.
- Scott R. Shannon, Image of the 9 12-faced polyhedra. None of these are visible on the surface.
- Scott R. Shannon, Image of all 12999 polyhedra. The polyhedra are colored red, orange, yellow, green for face counts 4 to 7 respectively. The polyhedra with 8, 9 and 12 faces are not visible on the surface.
- Scott R. Shannon, Image of all 12999 polyhedra, exploded. Each polyhedron has been moved away from the origin by a distance proportional to the average distance of its vertices from the origin. Some of the 8-, 9- and 12-faced polyhedra can now be seen.
- Eric Weisstein's World of Mathematics, Truncated Tetrahedron.
- Wikipedia, Truncated tetrahedron.
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