Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AV GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 2√2, 4, 4√2, 8, 12, 14√2, 17√2, 28, 34, 28√2, 34√2, 42√2, 76, 90, 104, 76√2, 118, 90√2, 180, 135√2.

Code: 1805 0 90 1354 135 135 1183 270 152 176 135 135 347 152 152 340 186 152 424 228 110 766 194 76 284 180 90 140 208 118 121 220 118 85 220 110 45 220 106 44 224 106 24 222 104 1043 194 0 287 194 104 905 0 0 904 90 0 765 194 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)