Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:186BH GHM

Order: 20

Horizontal side: 186 Vertical side: 186

Elements: 6, 5√2, 6√2, 12, 12√2, 20√2, 30, 25√2, 40, 29√2, 30√2, 35√2, 50, 58, 64, 70, 58√2, 64√2, 116, 122.

Code: 1225 0 64 1161 116 186 505 116 136 701 186 186 302 146 106 254 141 111 200 166 136 56 141 111 407 146 116 586 128 58 303 146 76 67 116 76 66 116 70 125 122 64 124 134 64 647 0 64 640 64 64 354 99 29 296 99 29 585 128 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)