Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:190AE GHM
Order: 20
Horizontal side: 190 Vertical side: 190
Elements: 5√2, 7√2, 10, 9√2, 18, 18√2, 25√2, 36, 40, 35√2, 56, 40√2, 45√2, 70, 56√2, 80, 60√2, 94, 67√2, 75√2.
Code: 752 75 115 701 70 190 352 105 155 604 130 130 676 123 123 250 105 155 103 80 120 452 125 85 361 116 130 182 134 112 74 123 123 54 75 115 803 80 40 183 134 94 562 190 56 94 125 85 943 134 0 563 190 0 405 0 0 404 40 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)