Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:328AN GHM
Order: 20
Horizontal side: 328 Vertical side: 328
Elements: 4√2, 8, 8√2, 16, 16√2, 22√2, 32, 44, 56, 49√2, 60√2, 88, 66√2, 98, 120, 93√2, 142, 120√2, 186, 164√2.
Code: 1865 0 142 1644 164 164 1206 208 208 443 208 164 1205 208 88 224 186 142 666 142 98 1425 0 0 934 93 49 496 93 49 985 142 0 565 208 32 604 268 28 883 328 0 321 240 32 162 256 16 161 256 32 82 264 24 81 264 32 42 268 28
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)