Fig. No. 3 shows the electron microscope image of the fracture surface of a spherical foam glass sample made of sintered coloured waste glass powder (0≤Φ≤125μ), whose density is ρ=1.75gr / cm³ . During sintering the maximum temperature is held for 11 minutes at 960°C.

Fig No. 3. Fracture surface of a spherical foam glass sample at scale 392 : 1

Using X-ray investigation it was possible to determine that the sample under consideration here contained approximately 10 + 15 % devitrite and traces of cristobalite¹⁾ . Based on a thin microsection, the mean free distance of the spherical bubbles of the spherical foam glass sample shown here was determined at 80 μ .

An analysis of the section of the polyhedron foam glasses produced by us generally shows the structure represented in Fig. No. 4.

Fig No. 4  section of a coarse-celled polyhedron foam glass sample

¹⁾ SiO₂. is polymorphous and for the reason occurs naturally in three crystalline forms:

• 1)as  quartz
• 2)as cristobalite (cubic) and
• 3)as tridymite (hexagonal).

This is a section of the same foam glass cuboid as shown in Fig. No. 1. Here you can see the richness of forms of the innumerable polyhedron cell bubbles!

In order to express that the cell walls are comprised of fixed shape and low capillary space spherical foam glass, in future we will refer to them as films ¹⁾.

Images of microsections through a given polyhedron foam glass sample using polarised light show that the glass base material of the cell wall films contain many small embedded crystals as well as chemically unreacted expanding agent.

Since in the original glass melt - from which the polyhedron foam glass is expanded - surface tensions are active, the physical principles for liquid polyhedron foams, as described in section 1.2, can also be used for the solidified polyhedron foam glass.  For this reason it can be asserted that in statistical mean the morphology of all given two-dimensional sections through a random polyhedron foam glass sample can be expressed using the following idealised sketch - in accordance with the principles of J. Plateau.

The centre surfaces of all cell wall films of the polyhedron foam glass form a series of surfaces which is called a cell structure. It is formed from the surfaces of the most diverse convex polyhedrons which completely pervade the space according to the rules. These bodies will be referred to hereafter as elementary polyhedron or base polyhedron of the cell structure of the polyhedron foam glass!¹⁾

The morphology is based on the idea that the diverse world of shapes of the elementary polyhedra of the cell structure of a given polyhedron foam glass sample are only derivatives of one archetype (2). According to their school of thought it would now be necessary to search for the archetypes of all individual elementary polyhedra of the cell structure of the polyhedron foam glass.

The following requirements are placed on the archetypes of the base polyhedron of the cell structure of the polyhedron foam glass:

Fig. No. 5a shows the α - tetradecahedron of W. Kelvin (3), which can be adopted as the base polyhedron of an ideal polyhedron foam glass.

Fig. No. 5  The α - tetradecahedron and the β - tetradecahedron

This polyhedron is closely related to the truncated octahedron¹⁾. It has eight double curved hexagonal surfaces and six square flat surfaces. All 36 edge lines of the α- tetradecahedron are congruent flat curves. The curved surfaces (minimum surfaces) are a requirement of the minimum of the surface energy.

In a polyhedron foam glass, whose cell structure is composed of many such identical elementary polyhedra, three cell wall films meet at an intersection angle of 120° at an “edge”, one is four-sided and two are hexagonal. This ideal foam glass meets all the conditions of J. Plateau.

The polyhedron forms the basis for the model polyhedron foam glasses “TOP” and “ORTHO” which are dealt with later.

Matzke and Nestler showed that the static distribution of the polyhedron surfaces of the cell structure of soap bubble packing differs significantly  from that of ideal foams, which have cell structures, which are comprised of many

Kelvin polyhedra. Thus they identified a preference for pentagonal side surfaces.

The following summary from R.E. Williams is intended to illustrate this:

For this reason R.E. Williams in 1968 suggested the β - tetradecahedron as the base polyhedron for the cell structure of natural foams (4)!

Fig. No. 5c shows the new polyhedron of R.E. Williams, which can be viewed as the elementary polyhedron of an ideal polyhedron foam glass consistent with the base principles of J. Plateau. It can be mechanically derived from the Kelvin polyhedron, by taking one “edge” of two of its neighbouring six-sided surfaces - including the “edges” connecting at its ends - (see Fig. 5a), turning the whole thing and joining it together again. The resulting polyhedron (Fig. No. 5b) with four four-sided, four five-sided and six six-sided surfaces can also pervade the space. The same operation is carried out with the corresponding group of “edges” on the opposite side of the polyhedron. This leads to the body (β -tetradecahedron) on Fig. No. 5c.

This transformation retains the same number of 14 surfaces, 24 vertices and 36 “edges” as the α - tetradecahedron and the corner angles remain 109°28'. As the table above show, the percentage distribution of the surfaces corresponds roughly to the conditions in nature.