Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:175AA GHM

Order: 20

Horizontal side: 175 Vertical side: 175

Elements: 2, 2√2, 4, 4√2, 23, 23√2, 38, 45, 46, 47, 49, 38√2, 57, 61, 45√2, 46√2, 76, 57√2, 61√2, 76√2.

Code: 765 0 99 764 76 99 230 152 175 231 175 175 460 129 152 461 175 152 450 83 106 451 128 106 477 128 106 493 175 57 385 0 61 384 38 61 615 0 0 614 61 0 40 122 61 41 126 61 22 128 59 21 128 61 570 118 57 571 175 57

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)