A119602 Number of nonisomorphic polytetrahedra with n identical regular tetrahedra connected face-to-face or edge-to-edge (chiral shapes counted twice).

1, 1, 2, 7, 39

Offset: 0

Author

Jonathan Vos Post, Jun 02 2006

Keywords

• nonn
• more

Comments

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.

Examples

			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.
		

Links

• 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

Crossrefs

Cf. A000577, A000105.