Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:192AP GHM
Order: 20
Horizontal side: 192 Vertical side: 192
Elements: 4, 11√2, 15√2, 20√2, 30, 40, 29√2, 30√2, 45, 38√2, 40√2, 58, 60, 67, 49√2, 76, 58√2, 94, 67√2, 76√2.
Code: 765 0 116 764 76 116 206 132 172 407 152 192 406 152 152 943 132 78 605 132 112 582 58 58 384 38 78 305 132 82 304 162 82 453 192 67 45 132 78 154 147 67 494 87 29 110 136 78 670 125 67 671 192 67 583 58 0 292 87 29
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)