Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328AV GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 2√2, 4, 4√2, 6√2, 8√2, 19√2, 38, 38√2, 56, 48√2, 56√2, 84, 112, 84√2, 122, 103√2, 160, 168, 122√2, 206.
Code: 2065 0 122 1681 168 328 1125 168 216 1601 328 328 565 168 160 564 224 160 480 280 216 80 232 168 64 238 162 46 240 164 847 244 168 846 244 84 26 238 162 45 240 160 384 206 122 383 244 122 1225 0 0 1224 122 0 196 225 103 1030 225 103
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)