Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:234CF GHM
Order: 20
Horizontal side: 234 Vertical side: 234
Elements: 4√2, 8, 8√2, 9√2, 12√2, 18, 16√2, 20√2, 21√2, 40, 30√2, 40√2, 57, 60, 78, 96, 78√2, 117, 156, 117√2.
Code: 1565 0 78 1174 117 117 1173 234 117 304 147 87 210 177 117 571 234 117 96 147 87 187 156 96 963 174 0 82 182 88 124 186 84 160 198 96 83 182 80 42 186 84 402 214 40 401 214 80 202 234 60 785 0 0 784 78 0 603 234 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)