Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:74AC GHM

Order: 20

Horizontal side: 74 Vertical side: 74

Elements: 2√2, 4, 4√2, 7, 5√2, 8, 8√2, 14, 16, 17, 20, 24, 17√2, 28, 20√2, 30, 22√2, 27√2, 40, 30√2.

Code: 305 0 44 304 30 44 20 60 74 141 74 74 283 58 44 47 58 72 40 62 72 87 58 68 80 66 68 167 58 60 403 74 20 222 22 22 174 17 27 173 34 27 247 34 44 54 22 22 270 27 27 71 34 27 204 54 0 203 74 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)