Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:236AB GHM

Order: 19

Horizontal side: 236 Vertical side: 236

Elements: 10√2, 20, 20√2, 34, 40, 50, 58, 42√2, 45√2, 68, 50√2, 76, 84, 65√2, 68√2, 76√2, 110, 84√2, 126.

Code: 845 0 152 844 84 152 1263 168 110 687 168 236 686 168 168 585 168 110 762 76 76 424 42 110 341 76 110 1105 76 0 654 141 45 200 206 110 201 226 110 102 236 100 506 186 50 456 141 45 407 186 90 763 76 0 505 186 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)