Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:186BB GHM

Order: 20

Horizontal side: 186 Vertical side: 186

Elements: 2√2, 4, 4√2, 26, 23√2, 26√2, 27√2, 46, 50, 52, 54, 44√2, 46√2, 48√2, 52√2, 56√2, 82, 86, 88, 90.

Code: 907 0 186 460 90 186 461 136 186 232 159 163 501 186 186 270 159 163 446 0 96 887 44 140 26 130 138 47 132 140 863 130 52 562 186 82 541 186 136 482 48 48 823 186 0 44 48 48 520 52 52 521 104 52 262 130 26 261 130 52

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)