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We show a simple method to generate polyominoes and polyiamonds that produce isohedral tilings with p3, p4 or p6 rotational symmetry by using n line segments between lattice points on a regular hexagonal, square and triangular lattice, respectively. We exhibit all possible tiles generated by this algorithm up to n = 9 for p3, n = 8 for p4, and n = 13 for… (More)
We describe computer algorithms that can enumerate and display, for a given n > 0 (in theory, of any size), all n-ominoes, n-iamonds, and n-hexes that can tile the plane using only rotations; these sets necessarily contain all such tiles that are fundamental domains for p4, p3, and p6 isohedral tilings. We display the outputs for small values of n. This… (More)
Received (received date) Revised (revised date) Communicated by (Name) We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and… (More)
In this paper, we consider two classes of polyhedra. One is the class of polyhedra of maximal volume with n vertices that are inscribed in the unit sphere of R 3. The other class is polyhedra of minimal volume with n vertices that are circumscribed about the unit sphere of R 3. We construct such polyhedra for n up to 30 by a computer aided search and… (More)
Some classes of I-factorizations of complete graphs are known. They are GK 2n , AK 2n , W K 2n and their variations, and automorphism-free I-factorizations. In this paper, for any positive integer t, we construct new I-factorizations N t K 2n which are defined for all 2n with 2n ~ 6t. They also have some variations.