Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:312BC GHM

Order: 20

Horizontal side: 312 Vertical side: 312

Elements: 4, 4√2, 8, 8√2, 14, 16, 18, 16√2, 32, 23√2, 32√2, 46, 46√2, 110, 78√2, 101√2, 110√2, 156, 202, 156√2.

Code: 2025 0 110 1564 156 156 1563 312 156 464 202 110 166 232 140 325 248 124 324 280 124 786 234 78 86 224 132 165 232 124 46 220 128 85 224 124 183 220 110 45 220 124 147 220 124 236 211 101 467 234 124 1105 0 0 1104 110 0 1010 211 101

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)