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- Hiroshi Fukuda, Nobuaki Mutoh, Gisaku Nakamura, Doris Schattschneider
- Graphs and Combinatorics
- 2007

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)

- Hiroshi Fukuda, Nobuaki Mutoh, Gisaku Nakamura, Doris Schattschneider
- KyotoCGGT
- 2007

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)

- Hiroshi Fukuda, Chiaki Kanomata, Nobuaki Mutoh, Gisaku Nakamura, Doris Schattschneider
- Symmetry
- 2011

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)

- Midori Kobayashi, Nobuaki Mutoh, Kiyasu-Zen'iti, Gisaku Nakamura
- Ars Comb.
- 2002

- Jin Akiyama, Rika Mochizuki, Nobuaki Mutoh, Gisaku Nakamura
- JCDCG
- 2002

- Nobuaki Mutoh
- JCDCG
- 2002

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)

- Hiroshi Fukuda, Chiaki Kanomata, Nobuaki Mutoh, Gisaku Nakamura, Doris Schattschneider
- Symmetry
- 2011

- Midori Kobayashi, Brendan D. McKay, +14 authors Rika Mochizuki
- 2014

- Midori Kobayashi, Nobuaki Mutoh, Kiyasu-Zen'iti, Gisaku Nakamura
- Australasian J. Combinatorics
- 2002

A double Dudeney set in K n is a multiset of Hamilton cycles in K n having the property that each 2-path in K n lies in exactly two of the cycles. In this paper, we construct a double Dudeney set in K n when n = p 1 p 2 · · · p s + 2, where p 1 , p 2 ,. .. , p s are different odd prime numbers and s is a natural number.