Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:234BV GHM

Order: 20

Horizontal side: 234 Vertical side: 234

Elements: 1, 4, 3√2, 5, 4√2, 6, 8, 11√2, 17, 22, 39, 28√2, 56, 78, 56√2, 100, 78√2, 89√2, 156, 117√2.

Code: 1565 0 78 1174 117 117 896 145 145 280 145 145 391 156 117 177 156 117 63 173 111 55 173 112 17 173 112 40 174 112 41 178 112 562 234 56 110 167 111 34 170 108 81 178 108 227 156 100 1003 178 0 785 0 0 784 78 0 563 234 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)