Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:272BC GHM

Order: 20

Horizontal side: 272 Vertical side: 272

Elements: 4, 4√2, 8, 6√2, 12, 12√2, 18, 18√2, 25√2, 36, 50, 68, 86, 100, 118, 86√2, 93√2, 100√2, 154, 172.

Code: 1725 0 100 1541 154 272 1187 154 272 936 179 179 250 179 179 365 154 118 501 204 154 685 204 86 184 172 100 60 190 118 120 184 112 121 196 112 85 196 104 45 196 100 44 200 100 183 204 86 1005 0 0 1004 100 0 860 186 86 861 272 86

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)