Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:190AK GHM

Order: 20

Horizontal side: 190 Vertical side: 190

Elements: 11, 14, 11√2, 12√2, 22, 24, 33, 38, 31√2, 33√2, 48, 52, 38√2, 59, 48√2, 52√2, 76, 83, 76√2, 95√2.

Code: 952 95 95 831 83 190 597 83 190 480 142 190 481 190 190 110 94 142 111 105 142 337 105 142 336 105 109 527 138 142 526 138 90 245 83 107 221 105 131 124 95 95 310 107 107 145 138 76 760 76 76 761 152 76 382 190 38 383 190 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)