Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:100AH1of2 GHM
Order: 20
Horizontal side: 100 Vertical side: 100
Elements: 4, 4√2, 8, 8√2, 12, 14, 10√2, 14√2, 20, 15√2, 17√2, 28, 20√2, 30, 25√2, 28√2, 40, 30√2, 43√2, 50√2.
Code: 502 50 50 434 43 57 140 86 100 141 100 100 86 64 78 287 72 86 286 72 58 46 60 74 85 64 70 176 43 57 45 60 70 252 85 45 121 72 70 100 50 50 150 85 45 403 40 0 202 60 20 201 60 40 300 70 30 301 100 30
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)