Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:368AV GHM
Order: 20
Horizontal side: 368 Vertical side: 368
Elements: 10, 10√2, 22√2, 60, 68, 60√2, 67√2, 68√2, 104, 77√2, 112, 114, 120, 134, 136, 144, 112√2, 164, 120√2, 188.
Code: 1887 0 368 1200 188 368 1201 308 368 602 368 308 601 368 368 1643 368 144 686 0 180 1367 68 248 1143 204 134 1047 204 248 685 0 112 107 204 144 100 214 144 774 291 67 1443 368 0 220 90 134 1341 224 134 672 291 67 1127 0 112 1120 112 112
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)