Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:192AZ GHM

Order: 20

Horizontal side: 192 Vertical side: 192

Elements: 10, 18, 19√2, 28, 30, 38, 28√2, 42, 30√2, 32√2, 34√2, 56, 42√2, 60, 64, 60√2, 66√2, 94, 98, 75√2.

Code: 987 0 192 666 32 126 947 98 192 756 117 117 320 32 126 190 117 117 387 98 98 286 108 70 565 136 42 647 0 94 340 64 94 103 108 60 285 108 42 306 0 30 607 30 60 600 90 60 181 108 60 424 150 0 423 192 0 305 0 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)