Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AF GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 5√2, 10, 10√2, 16√2, 28, 28√2, 52, 56, 52√2, 78, 82, 84, 62√2, 104, 110, 78√2, 114, 82√2, 136, 109√2.

Code: 1145 0 156 1094 109 161 1043 218 166 522 270 218 521 270 270 1363 270 82 56 109 161 105 114 156 104 124 156 563 134 110 847 134 166 782 78 78 624 62 94 166 62 94 1105 78 0 284 106 82 283 134 82 824 188 0 823 270 0 783 78 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)