|There are a potential 8 tiles resulting from the application of the grouped element technique to the order 3 symmetric tile, but they come in complementary pairs each of which is the other rotated by 180°, which reduces the number of candidates to 4. Two of these are implementations of the symmetric tile, which leaves us with 2 order 3 demisymmetric tiles.|
|There are a potential 32 tiles resulting from the application of the group element technique to the order 5 symmetric tiles, but this is reduced to 16 by elimination of one copy of each complementary pair, to 12 by elimination of implementations of the symmetric tiles, and to 10 by elimination of order 5 dissections of the order 3 demisymmetric tiles, so there are 10 order 5 demisymmetric tiles.|
|With an order 7 dissection the number of potential tiles rises to
128. This is reduced to 64 (8 groups of 8) by elimination of one copy
of each complementary pair, and to 56 by elimination of implementations
of the symmetric tile (1 group). In the case of the
2c+2c4+2c7+c9 dissection the remaining
7 groups are
Thus there are are a total of 52 2c+2c4+2c7+c9 demisymmetric tiles.
Thus there are a total of 48 4c2+c3+2c4 demisymmetric tiles.
© 2015 Stewart R. Hinsley