Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:224AH4of4 GHM

Order: 20

Horizontal side: 224 Vertical side: 224

Elements: 1√2, 2, 2√2, 12, 12√2, 24, 24√2, 36, 29√2, 31√2, 48, 58, 54√2, 55√2, 56√2, 58√2, 110, 112, 114, 112√2.

Code: 1147 0 224 540 114 224 554 169 169 566 168 168 363 60 134 487 60 170 296 79 141 587 108 170 580 166 170 21 168 170 12 169 169 310 79 141 240 24 134 241 48 134 122 60 122 121 60 134 24 110 110 1120 112 112 1121 224 112 1107 0 110

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)