Primitive Perfect Isosceles Right Triangled Square

Title: _d 19:236BD GHM

Order: 19

Horizontal side: 236 Vertical side: 236

Elements: 1, 8, 8√2, 16, 24, 24√2, 27√2, 28√2, 52, 53, 38√2, 54, 56, 64, 91, 118, 91√2, 145, 118√2.

Code: 1455 0 91 1184 118 118 1183 236 118 274 145 91 286 144 90 565 172 62 641 236 118 917 0 91 910 91 91 531 144 91 17 144 91 525 144 38 244 196 38 243 220 38 87 220 62 80 228 62 167 220 54 543 236 0 384 182 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)