Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:148AB GHM

Order: 20

Horizontal side: 148 Vertical side: 148

Elements: 6, 8√2, 12, 16, 18, 16√2, 24, 17√2, 30, 32, 34, 28√2, 40, 46, 48, 34√2, 56, 57√2, 62√2, 74√2.

Code: 742 74 74 624 62 86 323 124 116 162 140 132 241 148 148 163 140 116 82 148 124 563 148 68 303 92 86 487 92 116 121 74 86 465 74 40 181 92 86 176 57 57 284 120 40 346 114 34 570 57 57 401 114 40 67 114 40 345 114 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)