Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:234BQ GHM
Order: 20
Horizontal side: 234 Vertical side: 234
Elements: 5, 5√2, 7√2, 10, 9√2, 14, 15, 14√2, 15√2, 16√2, 32, 24√2, 62, 78, 62√2, 94, 78√2, 86√2, 156, 117√2.
Code: 1565 0 78 1174 117 117 866 148 148 240 148 148 76 117 117 145 124 110 144 138 110 50 152 124 51 157 124 157 157 124 156 157 109 622 234 62 90 147 119 101 157 119 321 156 110 162 172 94 943 172 0 785 0 0 784 78 0 623 234 0
The properties below may precede order:side in a tiling's title:
- c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
- d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
- e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
- i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
- r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.
Credit for Discovery
Just three people are credited with the discovery of Primitive Perfects:
Geoffrey H. Morley (GHM, England)
Jasper D. Skinner, II (JDS, United States)
William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)