A343209 -id:A343209 - cp's OEIS frontend

A343210 Number of nonisomorphic unfoldings of the n-th Johnson solid.

8, 15, 308, 3030, 29757, 7825005, 63, 448, 3116, 3421, 40321, 9, 99, 156, 2010, 25574, 13041, 268260, 28427091, 2982139245, 822310337549, 6193152, 1935360000, 599660087082, 170242287969600, 152, 27195, 1867560, 1934427, 125939163, 132627603, 74520844992

Offset: 1

Pontus von Brömssen, Apr 08 2021

Unfoldings with overlaps are allowed.

Terms are taken from the paper by Horiyama and Shoji.

			The gyrobifastigium (J26) has a(26) = 152 nonisomorphic unfoldings.

Pontus von Brömssen, Table of n, a(n) for n = 1..92
Takashi Horiyama and Wataru Shoji, The number of different unfoldings of polyhedra, The 29th European Workshop on Computational Geometry, Technische Universität Braunschweig 2013, 143-146. [Apparently, two pairs of Johnson solids have switched numbers in Table 2, namely J32 <-> J33 and J40 <-> J41.]
Wikipedia, List of Johnson solids

Cf. A242731, A343209.

A343213 Number of spanning trees of the graphs of the platonic solids sorted by the number of faces.

Original entry on oeis.org

16, 384, 384, 5184000, 5184000

Offset: 1

Pontus von Brömssen, Apr 08 2021

Cf. A053572, A343209.

A343432 Sorted numbers of spanning trees in the graphs of the Archimedean solids.

Original entry on oeis.org

6000, 331776, 32400000, 101154816, 301056000000, 89904012853248, 208971104256000, 12418325780889600, 4982259375000000000, 375291866372898816000, 201550864919150779950956544000, 438201295386966498858139607040000000, 21789262703685125511464767107171876864000

Offset: 1

Pontus von Brömssen, Apr 15 2021

The duals (Catalan solids) have the same number of spanning trees as their Archimedean counterparts.

			The solids are in order:
  truncated tetrahedron (6000),
  cuboctahedron (331776),
  truncated cube (32400000),
  truncated octahedron (101154816),
  rhombicuboctahedron (301056000000),
  snub cube (89904012853248),
  icosidodecahedron (208971104256000),
  truncated cuboctahedron (12418325780889600),
  truncated dodecahedron (4982259375000000000),
  truncated icosahedron (375291866372898816000),
  rhombicosidodecahedron (201550864919150779950956544000),
  snub dodecahedron (438201295386966498858139607040000000),
  truncated icosidodecahedron (21789262703685125511464767107171876864000).

Cf. A343209, A343213, A343433.

cp's OEIS Frontend

A343210 Number of nonisomorphic unfoldings of the n-th Johnson solid.

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A343213 Number of spanning trees of the graphs of the platonic solids sorted by the number of faces.

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A343432 Sorted numbers of spanning trees in the graphs of the Archimedean solids.

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Author

Keywords

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