Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:204AC1of4 GHM
Order: 20
Horizontal side: 204 Vertical side: 204
Elements: 3√2, 8√2, 16, 20, 16√2, 20√2, 32, 24√2, 40, 32√2, 46, 40√2, 46√2, 66, 86, 92, 66√2, 69√2, 72√2, 92√2.
Code: 925 0 112 924 92 112 200 184 204 201 204 204 246 140 160 402 204 144 401 204 184 80 140 160 863 132 66 167 132 152 160 148 152 726 132 72 322 164 104 321 164 136 465 0 66 464 46 66 32 135 69 690 135 69 665 0 0 664 66 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)