As from 1989 Heinz Schumann ([SCHUMANN 1990], [SCHUMANN 1989]) has made experiments in class that can be copied easily. You take equilateral triangles made of card board with a minimum size of 5 cm and cut their corners in a rhomboid way as referred to in the second sketch below.
Schumann calls the solids made up of these parts "DELTAEDER" (in this context "deltahedrons"), according to the form of the Greek delta. In this script I will use the term deltahedron both for the individual parts and the ready-made solids. Of course you can also construct solids consisting of squares, pentagons etc in the same way.
Sequence of building in class:
On building models pupils can be shown excellently how much better and faster a group can produce a number of models than a lot of individual students: First - as an experiment - each student is to construct and cut out one or two deltahedrons.
Then the sequence of work is analysed:
Construction of an equilateral triangle, construction of the rhomboid corners, then carve the vertices, cut out the rhomboid corners and fold the three vertices. Look at the sketch.
In order to make modelling more effective and preciser, each member of a group of three to five students concentrates on one or two procedures. This kind of assembly-line-work simulates real production (possibly together with another subject such as economic geography.)

After each group has produced approximately 100 (!!) parts the proper geometry class starts. The students can build together the single deltahedron-parts that form solids. The rubber-rings appear outside which makes the ready-made models look fascinating. According to Schumann there are only 8 convex deltahedrons, among them 3 of the Platonic solids: tetrahedron, octahedron, icosahedron. After the production of the deltahedron-parts and the distribution of about 135 rubber-rings the task for each individual group is to build as many different solids as possible. As students try to excel each other in building complicated constructions, it is better to interrupt the experiment after the building of the first non-convex solids to be able to give a definition (i.e. no vertices inside the solids). From then on only non-convex solids are to be built. By cutting out other polygons (e.g. pentagons, squares) with similar tabs (and rhomboid corners) other solids can be built as well. It is faster to cut out the deltaeder-parts from long card board stripes (width about 8 cm), whereby only two cuts are necessary to get one triangle (deltaeder-part). Otherwise the template at the end of this script can be used.