Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:312BP GHM

Order: 20

Horizontal side: 312 Vertical side: 312

Elements: 1√2, 2, 2√2, 4, 4√2, 7√2, 14, 11√2, 14√2, 28, 25√2, 39√2, 78, 106, 78√2, 103√2, 106√2, 156, 206, 156√2.

Code: 2065 0 106 1564 156 156 1563 312 156 394 195 117 283 234 128 787 234 156 786 234 78 116 195 117 145 206 114 144 220 114 256 209 103 42 210 110 74 213 107 43 210 106 22 212 108 23 212 106 12 213 107 1065 0 0 1064 106 0 1030 209 103

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)