Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:264AD1of2 GHM

Order: 19

Horizontal side: 264 Vertical side: 264

Elements: 2, 2√2, 4, 4√2, 6, 14, 14√2, 28, 28√2, 56, 49√2, 76, 55√2, 56√2, 104, 132, 104√2, 160, 132√2.

Code: 1605 0 104 1324 132 132 1323 264 132 284 160 104 283 188 104 142 202 118 761 264 132 143 202 104 42 206 114 43 206 110 22 208 112 23 208 110 562 264 56 67 202 110 556 153 55 1047 0 104 1040 104 104 494 153 55 563 264 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)