Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:192AS GHM
Order: 20
Horizontal side: 192 Vertical side: 192
Elements: 10√2, 11√2, 20, 15√2, 25, 30, 40, 30√2, 38√2, 56, 40√2, 60, 65, 49√2, 76, 78, 56√2, 58√2, 68√2, 76√2.
Code: 765 0 116 764 76 116 653 152 127 407 152 192 406 152 152 255 152 127 490 87 127 601 147 127 302 177 97 301 177 127 152 192 112 582 58 58 384 38 78 566 136 56 201 58 78 102 68 68 781 136 78 112 147 67 680 68 68 565 136 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)