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A339538
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Irregular table read by rows: The number of k-faced polyhedra, where k>=4, created when an elongated n-bipyramid, with faces that are squares and equilateral triangles, is internally cut by all the planes defined by any three of its vertices.
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1
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258, 336, 60, 424, 584, 208, 48, 8, 8830, 16090, 12210, 5040, 1210, 260, 80, 10
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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3,1
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COMMENTS
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For an elongated n-bipyramid with faces that are squares and equilateral triangles, formed by joining the two halves of an n-gonal bipyramid by an n-prism, 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 k-faced polyhedra, where k>=4, for elongated n-bipyramids where 3 <= n <= 5. These three elongated bipyramids are the only possible elongated bipyramids that are Johnson solids, i.e., their faces are all regular polygons.
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LINKS
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EXAMPLE
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The elongated 5-bipyramid has 12 vertices, 25 edges and 15 faces (5 squares and 10 equilateral triangles). It is cut by 112 internal planes defined by any three of its vertices, resulting in the creation of 43730 polyhedra.
The 11 faced polyhedra are unusual in that all 10 are visible on the surface; most polyhedra cut with their own planes have the resulting polyhedra with the most faces near the center of the original polyhedra and are thus not visible on its surface.
No polyhedra with 12 or more faces are created.
The table is:
258, 336, 60;
424, 584, 208, 48, 8;
8830, 16090, 12210, 5040, 1210, 260, 80, 10;
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CROSSREFS
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KEYWORD
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nonn,fini,full,tabf
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AUTHOR
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STATUS
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approved
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