

A119602


Number of nonisomorphic polytetrahedra with n identical regular tetrahedra connected facetoface or edgetoedge (chiral shapes counted twice).


2




OFFSET

0,3


COMMENTS

Polytetrahedra are a 3dimensional generalization of polyiamonds, composed of unit regular tetrahedra in Euclidean 3space.  Peter Kagey, Aug 05 2019, adapted from comment by Jonathan Vos Post.


REFERENCES

Jonathan Vos Post, Polytetrahedra, preprint, Draft 4.0, approx. 6750 words, 15 pages, available as Word file by email upon request.


LINKS

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 LongRange 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, BoerdijkCoxeter helix and biological helices, Eur. Phys. J. B 12, 309318.
Jonathan Vos Post, Original example for entry.
Eric Weisstein et al., Tetrahedron.
Wikipedia, Polyiamond
Wikipedia, Deltahedron


EXAMPLE

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.


CROSSREFS

Cf. A000577, A000105.
Sequence in context: A222034 A337685 A014058 * A121752 A054133 A330470
Adjacent sequences: A119599 A119600 A119601 * A119603 A119604 A119605


KEYWORD

nonn,more


AUTHOR

Jonathan Vos Post, Jun 02 2006


STATUS

approved



