Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:256BD GHM

Order: 20

Horizontal side: 256 Vertical side: 256

Elements: 5, 6, 6√2, 20, 15√2, 25, 20√2, 30, 25√2, 58, 64, 70, 58√2, 61√2, 64√2, 70√2, 122, 128, 134, 128√2.

Code: 1347 0 256 616 73 195 1227 134 256 1286 128 128 156 58 180 305 73 165 586 0 122 202 78 160 51 78 165 257 78 165 250 103 165 203 78 140 707 58 140 706 58 70 62 134 134 1285 128 0 585 0 64 65 58 64 647 0 64 640 64 64

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)