Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272AM GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 17√2, 20√2, 30, 24√2, 34, 40, 48, 34√2, 66, 48√2, 51√2, 64√2, 66√2, 72√2, 102, 104, 84√2, 134, 102√2, 104√2.

Code: 1047 0 272 1046 0 168 1347 104 272 176 221 255 347 238 272 346 238 238 510 221 255 666 104 138 1027 170 204 1026 170 102 842 84 84 665 104 72 305 170 72 200 84 84 485 104 24 484 152 24 720 200 72 640 64 64 401 104 64 244 128 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)