Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:160AH GHM

Order: 20

Horizontal side: 160 Vertical side: 160

Elements: 5√2, 10, 16, 20, 16√2, 24, 20√2, 32, 24√2, 45, 32√2, 35√2, 55, 56, 60, 45√2, 64, 70, 60√2, 70√2.

Code: 705 0 90 704 70 90 200 140 160 201 160 160 160 120 140 161 136 140 242 160 116 241 160 140 643 104 60 322 136 92 321 136 124 563 160 60 452 45 45 354 35 55 50 40 60 604 100 0 603 160 0 101 45 55 555 45 0 453 45 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)