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A119602
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Number of nonisomorphic polytetrahedra with n identical regular tetrahedra connected face-to-face or edge-to-edge (chiral shapes counted twice).
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2
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OFFSET
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0,3
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COMMENTS
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Polytetrahedra are a 3-dimensional generalization of polyiamonds, composed of unit regular tetrahedra in Euclidean 3-space. - Peter Kagey, Aug 05 2019, adapted from comment by Jonathan Vos Post.
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REFERENCES
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Jonathan Vos Post, Polytetrahedra, preprint, Draft 4.0, approx. 6750 words, 15 pages, available as Word file by email upon request.
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LINKS
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Table of n, a(n) for n=0..4.
Andrew I. Campbell, Valerie J. Anderson, Jeroen S. van Duijneveldt and Paul Bartlett, Dynamical Arrest in Attractive Colloids: The Effect of Long-Range Repulsion, Phys. Rev. Lett. 94, 208301 (2005).
Peter Kagey, Examples of the seven shapes that can be constructed from three tetrahedra, with Mathematica code.
J. F. Sadoc, Boerdijk-Coxeter helix and biological helices, Eur. Phys. J. B 12, 309-318.
Jonathan Vos Post, Original example for entry.
Eric Weisstein et al., Tetrahedron.
Wikipedia, Polyiamond
Wikipedia, Deltahedron
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EXAMPLE
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For n = 1, the a(1) = 1 polytetrahedron is the tetrahedron itself.
For n = 2, the a(2) = 2 polytetrahedra are formed by either gluing two tetrahedra along a face (triangular bipyramid) or gluing two tetrahedra along an edge.
For n = 7, the a(3) = 7 polytetrahedra are given in the links section.
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CROSSREFS
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Cf. A000577, A000105.
Sequence in context: A106211 A222034 A014058 * A121752 A054133 A266310
Adjacent sequences: A119599 A119600 A119601 * A119603 A119604 A119605
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KEYWORD
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nonn,more
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AUTHOR
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Jonathan Vos Post, Jun 02 2006
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STATUS
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approved
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