Editing Modular origami (section)

==Modeling systems==
===Robert Neale's penultimate module===
Neale developed a system to model [[Equilateral|equilateral polyhedra]] based on a module with variable [[vertex (geometry)|vertex]] angles. Each module has two pockets and two tabs, on opposite sides. The angle of each tab can be changed independently of the other tab. Each pocket can receive tabs of any angle. The most common angles form polygonal faces:

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* 60 degrees ([[triangle]])
* 90 degrees ([[Square (geometry)|square]])
* 108 degrees ([[pentagon]])
* 120 degrees ([[hexagon]])
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Each module joins others at the vertices of a polyhedron to form a polygonal face. The tabs form angles on opposite sides of an edge. For example, a subassembly of three triangle corners forms a triangle, the most stable configuration. As the internal angle increases for squares, pentagons and so forth, the stability decreases.

Many polyhedra call for unalike adjacent polygons. For example, a [[Pyramid (geometry)|pyramid]] has one square face and four triangular faces. This requires hybrid modules, or modules having different angles. A pyramid consists of eight modules, four modules as square-triangle, and four as triangle-triangle.

Further polygonal faces are possible by altering the angle at each corner. The Neale modules can form any equilateral polyhedron including those having [[rhombus|rhombic]] faces, like the [[rhombic dodecahedron]].

===Mukhopadhyay module===
The Mukhopadhyay module can form any equilateral polyhedron. Each unit has a middle crease that forms an edge, and triangular wings that form adjacent stellated faces. For example, a cuboctahedral assembly has 24 units, since the [[cuboctahedron]] has 24 edges.
Additionally, [[bipyramids]] are possible, by folding the central crease on each module outwards or convexly instead of inwards or concavely as for the [[icosahedron]] and other stellated polyhedra. The Mukhopadhyay module works best when glued together, especially for polyhedra having larger numbers of sides.