Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:234BJ GHM

Order: 20

Horizontal side: 234 Vertical side: 234

Elements: 2, 2√2, 4, 4√2, 6√2, 14, 10√2, 20, 15√2, 19√2, 30, 24√2, 68, 78, 88, 68√2, 78√2, 83√2, 156, 117√2.

Code: 1565 0 78 1174 117 117 836 151 151 150 151 151 196 117 117 307 136 136 246 142 112 682 234 68 66 136 106 145 142 98 42 140 102 43 140 98 22 142 100 23 142 98 201 156 98 102 166 88 883 166 0 785 0 0 784 78 0 683 234 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)