Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:62AA GHM

Order: 19

Horizontal side: 62 Vertical side: 62

Elements: 1√2, 2, 2√2, 4, 4√2, 12, 14, 16, 12√2, 18, 14√2, 20, 22, 24, 18√2, 26, 22√2, 32, 25√2.

Code: 265 0 36 254 25 37 243 50 38 122 62 50 121 62 62 323 62 18 16 25 37 25 26 36 24 28 36 163 30 22 207 30 38 145 0 22 144 14 22 227 0 22 220 22 22 44 26 18 43 30 18 184 44 0 183 62 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)