Welcome to antitile’s documentation!

Antitile is a package for manipulation of polyhedra and tilings using Python. It is designed to work with [Antiprism] but can be used on its own.

The bulk of this package pertains to Goldberg-Coxeter operations, as described in its own section.

Indices and tables


[Deza2004]M. Deza and M. Dutour. Goldberg-Coxeter constructions for 3- and 4-valent plane graphs. The Electronic Journal of Combinatorics, 11, 2004. #R20.
[Deza2015]Michel-Marie Deza, Mathieu Dutour Sikirić, Mikhail Ivanovitch Shtogrin. (2015) Geometric Structure of Chemistry-Relevant Graphs: Zigzags and Central Circuits. Springer. pp 131-148. https://books.google.com/books?id=HLi4CQAAQBAJ&lpg=PA130&ots=ls1r5QkM51&dq=goldberg-coxeter&pg=PA130#v=onepage&q=goldberg-coxeter&f=false
[Altschuler]Altschuler, E. L. et al. 1997. Possible Global Minimum Lattice Configurations for Thomson’s Problem of Charges on a Sphere. Phys. Rev. Lett. 78, 2681. [http://dx.doi.org/10.1103/PhysRevLett.78.2681 doi:10.1103/PhysRevLett.78.2681] http://www.mcs.anl.gov/~zippy/publications/thomson/thomsonPRL.html
[Goldberg]Goldberg, M, 1937. A class of multi-symmetric polyhedra. Tohoku Mathematical Journal.
[Hart1997]Hart, G, 1997. Calculating Canonical Polyhedra. Mathematica in Education and Research, Vol 6 No. 3, Summer 1997, pp. 5-10.
[Hart2012]Hart, G, 2012. Goldberg Polyhedra. In Senechal, Marjorie. Shaping Space (2nd ed.). Springer. pp. 125–138. [http://dx.doi.org/10.1007/978-0-387-92714-5_9 doi:10.1007/978-0-387-92714-5_9].
[Kenner]Kenner, H, 1976. Geodesic Math and How to Use It. University of California Press.
[Schein]Schein & Gayed, 2014. Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses. PNAS, Early Edition [http://dx.doi.org/10.1073/pnas.1310939111 doi:10.1073/pnas.1310939111]
[Oosterom]Van Oosterom, A & Strackee, J, 1983. The Solid Angle of a Plane Triangle. IEEE Trans. Biom. Eng. BME-30 (2): 125–126. [http://dx.doi.org/10.1109/TBME.1983.325207 doi:10.1109/TBME.1983.325207].
[Folke]Eriksson, Folke (1990). “On the measure of solid angles”. Math. Mag. 63 (3): 184–187. doi:10.2307/2691141. JSTOR 2691141.
[Caspar]D.L.D. Caspar and A. Klug. Physical principles in the construction of regular viruses. In Cold Spring Harb Symp Quant Biol., volume 27, pages 1–24, 1962.
[Coxeter]H.S.M. Coxeter. Virus macromolecules and geodesic domes. In J.C. Butcher, editor, A spectrum of mathematics, pages 98–107. Oxford University Press, 1971.
[Coxeter8]H.S.M. Coxeter. Truncation. In Regular Polytopes, pages 145-164 3rd ed, Dover, 1973.
[Tarnai]T. Tarnai, F. Kovacs, P.W. Fowler, and S.D. Guest. Wrapping the cube and other polyhedra. Proceedings of the Royal Society A, 468:2652–2666, 2012.
[StamLoop]Jos Stam: Evaluation of Loop Subdivision Surfaces, Computer Graphics Proceedings ACM SIGGRAPH 1998,
[StamCatmull]Stam, J. (1998). “Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values”. Proceedings of the 25th annual conference on Computer graphics and interactive techniques - SIGGRAPH ‘98. pp. 395–404. doi:10.1145/280814.280945. ISBN 0-89791-999-8.
[HartPropeller]Hart, G. W. (2000) Sculpture Based on Propellorized Polyhedra. Proceedings of MOSAIC 2000, Seattle, Washington, August 2000, pp. 61-70. http://www.georgehart.com/propello/propello.html
[HartConway]Hart, G. W. Conway Notation for Polyhedra. http://www.georgehart.com/virtual-polyhedra/conway_notation.html