Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:368AE GHM
Order: 20
Horizontal side: 368 Vertical side: 368
Elements: 20√2, 30, 40, 31√2, 40√2, 60, 62, 76, 60√2, 92, 104, 76√2, 122, 124, 140, 152, 122√2, 123√2, 124√2, 154√2.
Code: 1542 154 214 1234 123 245 923 246 276 1227 246 368 1226 246 246 316 123 245 627 154 276 766 140 200 1525 216 124 301 246 276 1403 140 60 765 140 124 1047 140 124 1240 244 124 1241 368 124 607 0 60 600 60 60 404 100 20 403 140 20 204 120 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)