Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:186BP GHM

Order: 20

Horizontal side: 186 Vertical side: 186

Elements: 6, 6√2, 7√2, 12, 14, 12√2, 24, 17√2, 28, 24√2, 34, 48, 38√2, 55, 62, 76, 55√2, 62√2, 124, 131.

Code: 1315 0 55 1241 124 186 622 186 124 621 186 186 483 186 76 143 138 62 245 138 52 244 162 52 763 186 0 74 131 55 283 138 34 557 0 55 550 55 55 384 93 17 125 138 40 124 150 40 65 138 34 64 144 34 176 93 17 347 110 34

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)