Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:160AC GHM

Order: 20

Horizontal side: 160 Vertical side: 160

Elements: 8, 7√2, 8√2, 14, 16, 12√2, 16√2, 28, 24√2, 28√2, 33√2, 47, 52, 40√2, 61, 66, 47√2, 52√2, 66√2, 68√2.

Code: 665 0 94 664 66 94 246 108 136 282 160 132 281 160 160 686 40 68 162 124 120 406 120 92 163 124 104 82 132 112 83 132 104 522 160 52 124 120 92 472 47 47 334 33 61 70 40 68 141 47 61 615 47 0 523 160 0 473 47 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)