Haresh Lalvani

Architech Haresh Lalvani, designed a similar system, using regular polygons at vertices to define angles, specified as integers corresponding to internal angles.

Website: http://lalvanistudio.com/

Citations https://scholar.google.com/citations?user=Ms-KbScAAAAJ&hl=en

US Patent 5775040

• https://patents.google.com/patent/US5775040A/en 1996-1998 Non-convex and convex tiling kits and building blocks from prismatic nodes, 36 pages

Convex tiles

Concave tiles

More concave tiles

Concave tiles in a tiling

Girih App 

Stefan Hintz wrote Girih App for Macs, to generate Girih tiling patterns.

Website: http://hintz.bplaced.net/en/2015/art/girih-app/ and https://twitter.com/GirihApp

Zome

Website: http://www.zometool.com | Lesson plans

The word "zome" was coined in 1968 by Steve Durkee combining the words dome and zonohedron. Both the building and the learning tool are the brainchildren of inventor/designer Steve Baer, his wife, Holly, and associates. The overall shape of a connector node is that of a non-uniform small rhombicosidodecahedron, except that each face is replaced by a small hole. The ends of the struts are designed to fit in the holes of the connector nodes, allowing for syntheses of a variety of structures. The idea of shape-coding the three types of struts was developed by Marc Pelletier and Paul Hildebrandt. To create the "balls," or nodes, Pelletier and Hildebrandt invented a system of 62 hydraulic pins that came together to form a mold. The first connector node emerged from their mold perfectly on April 1, 1992.

Using 3 postions of struts (blue for rectangles, yellow for triangle holes and red or pentagonal holes.) Using these, zome can make angles of a regular triangle, square, pentagon, and hexagon in 2D. Struts have different edge lengths.

Zome nodes and struts

Regular polygons

Brain Flakes

Website: https://brainflakes.com/

Brain Flakes have 45 degree slots, so can make octatiles in 2D.