Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:234CK GHM

Order: 20

Horizontal side: 234 Vertical side: 234

Elements: 1√2, 2, 5√2, 10, 10√2, 15, 15√2, 30, 37, 41, 35√2, 38√2, 41√2, 76, 78, 80, 78√2, 117, 156, 117√2.

Code: 1565 0 78 1174 117 117 1173 234 117 384 155 79 373 193 80 412 234 76 411 234 117 16 155 79 27 156 80 803 158 0 105 158 70 104 168 70 150 178 80 151 193 80 785 0 0 784 78 0 763 234 0 352 193 35 54 163 65 301 193 65

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)