Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:216AJ GHM

Order: 20

Horizontal side: 216 Vertical side: 216

Elements: 5√2, 6√2, 10, 12, 10√2, 12√2, 15√2, 16√2, 24, 30, 32, 50, 56, 68, 80, 92, 68√2, 80√2, 136, 108√2.

Code: 1365 0 80 1084 108 108 923 216 124 166 108 108 327 124 124 56 151 119 107 156 124 106 156 114 507 166 124 563 216 68 150 151 119 126 124 92 245 136 80 301 166 104 805 0 0 804 80 0 123 160 68 62 166 74 680 148 68 681 216 68

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)