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A119602 Number of nonisomorphic polytetrahedra with n identical regular tetrahedra connected face-to-face or edge-to-edge (chiral shapes counted twice). 2
1, 1, 2, 7, 39 (list; graph; refs; listen; history; text; internal format)



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.


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


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


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.


Cf. A000577, A000105.

Sequence in context: A222034 A337685 A014058 * A121752 A054133 A330470

Adjacent sequences:  A119599 A119600 A119601 * A119603 A119604 A119605




Jonathan Vos Post, Jun 02 2006



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