Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:312AB1of2 GHM

Order: 20

Horizontal side: 312 Vertical side: 312

Elements: 8√2, 16, 16√2, 24, 28, 24√2, 25√2, 28√2, 48, 50, 39√2, 50√2, 78, 56√2, 78√2, 128, 156, 117√2, 131√2, 156√2.

Code: 1562 156 156 1314 131 181 500 262 312 501 312 312 560 212 262 481 260 262 242 284 238 241 284 262 282 312 234 281 312 262 166 268 222 1563 312 78 86 260 214 165 268 206 256 131 181 1287 156 206 396 117 117 1170 117 117 784 234 0 783 312 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)