The sphinx tile is composed of six identical triangles. It has the ability to tile itself. The number of different self-tilings as the order of the sphinx gets larger has recently been extended. The computing code that resulted from that effort (Walter Trump) morphed into a simple graphical user interface to tile any shape on the triangular grid with any shape. The graphics in this paper are from that program. After a year or two it begins to be difficult to know who contributed what originally.

New Ideas for the sphinx tile in these graphics:

1) Sphinx tile classification

2) Sphinx tile – 12 aspects (Trump)

3) Small shapes with multiple sphinx tilings

4) Sphinx dominoes

5) Sphinx tile polymerization

6) Examples of all 153 order 5 sphinx tilings ( OEIS ref)

7) Large shape with only one sphinx tiling

8) Hyper-packing the sphinx

9) Tiling with component triangle defects

10) Homogeneous sphinx tiling

11) cylindrical tiling (Trump)

12) Interlocking shapes

**References**

- http://oeis.org/search?q=sphinx+knecht&language=english&go=Search;
- Mathematical Models: Humanizing the Polyamonds, https://inderjtaneja.com/2019/03/14/mathematical-models-humanizing-the-polyiamonds/

Below are some examples:

**References**

- http://oeis.org/search?q=sphinx+knecht&language=english&go=Search;
- Mathematical Models: Humanizing the Polyamonds, https://inderjtaneja.com/2019/03/14/mathematical-models-humanizing-the-polyiamonds/