Edge Modules form the edges of a polyhedron. With the advent of the World Wide Web in 1994, many origamists started sharing their designs for free!

Penultimate Module by Robert Neal: Instructions by Jim Plank.

PhiZZ Module by Tom Hull: Instructions. Another set of Instructions.

Ow's Module by Francis Ow: Instructions.

Oxi Module by Michał Kosmulski: Instructions — I found it challenging to assemble models with these.

An Edge Module by Carmen Sprung: Instructions.

Many edge modules produce decorative and "flowery" models:

Arabesque by Mio Tsugawa: Instructions — More diagrams by Mio Tsugawa.

Chrysanthemum by Leroy: Instructions

There exist modules that constitute faces of a polyhedron instead of edges. However, the final models are hollow because not all faces are covered: Jitterbug Module by Tung Ken Lam: Instructions. Plane Sonobe: Instructions.

» Tomoko Fuse's Unit Origami: Multidimensional Transformations (1990, 240 pages) is a classic reference for Modular Origami. Her book contains many edge modules that yield beautiful models. See, for example, the "Open Frame I" and "Open Frame II" modules in the pictures above.

» Modular Origami Polyhedra by Lewis Simon, Bennett Arnstein & Rona Gurkewitz (1999, 64 pages).

Michał Kosmulski, Don Albert.