Biomedical Engineering Reference
In-Depth Information
(a)
(b)
Figure 6.17
(a) Open-celled cubic block [56]; (b) parallel plate model [30].
(a)
(b)
Figure 6.18
(a) Tetrakaidecahedron [30]; (b) pentagonal dodecahedron [30].
A different modeling approach is based on so-called polyhedral cells [30]. Typical
representatives are the tetrakaidecahedron, which is composed of six squares and
eight hexagons (cf. Figure 6.18(a)) and the pentagonal dodecahedron, which is
built up of 12 regular pentagons (cf. Figure 6.18(b)). It should be noted here
that only the tetrakaidecahedron is a true space-filling body and the pentagonal
dodecahedron does not pack properly unless distorted or combined with other
structures.
At the end of this section, let us in addition mention the geometrical model by Ko
[58] who considered geometrical shapes of interstices of hexagonal closest packing
and FCC closest packing of uniform spheres. His approach can be imagined
as a uniform expansion of each sphere so that a contacting surface becomes
flat and tangent to a contact point. Thus, each sphere becomes a polyhedron.
As an example, the hexagonal closest packing will deform each sphere into
trapezo-rhombic dodecahedron with six equilateral trapezoids and six congruent
rhombics. Most of the interstices are then squeezed to form 24 edges of such a
dodecahedron.
