Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:192AI GHM

Order: 20

Horizontal side: 192 Vertical side: 192

Elements: 4, 4√2, 11√2, 22, 16√2, 32, 36, 28√2, 44, 52, 37√2, 59, 44√2, 52√2, 74, 81, 59√2, 92, 100, 74√2.

Code: 745 0 118 744 74 118 1003 148 92 447 148 192 446 148 148 282 176 120 323 176 88 162 192 104 592 59 59 374 37 81 526 140 52 110 48 92 921 140 92 45 140 88 44 144 88 367 140 88 221 59 81 815 59 0 593 59 0 525 140 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)