Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:160AW GHM
Order: 20
Horizontal side: 160 Vertical side: 160
Elements: 12, 11√2, 12√2, 15√2, 24, 18√2, 20√2, 24√2, 40, 29√2, 42, 48, 35√2, 50, 40√2, 60, 70, 50√2, 90, 70√2.
Code: 907 0 160 700 90 160 701 160 160 206 0 70 407 20 90 400 60 90 294 89 61 180 118 90 421 160 90 116 89 61 127 100 72 126 100 60 247 112 72 240 136 72 352 35 35 605 100 0 154 35 35 500 50 50 501 100 50 481 160 48
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)