| volume |
v |
the volume of a cell - Ev=λ-1,
λ is the intensity of the tessellation generating point
process, all numerical results in the tables relate to unit tessellations (λ=1) |
| surface |
s |
the surface of a cell - the area of the cell boundary |
| perimeter |
p |
the perimeter of a cell - the total length of the cell edges |
| mean breadth |
w |
the mean breadth of a cell (also mean Feret diameter, calliper diameter)
- the mean distance of parallel support planes forming an isotropic system (for convex
sets only - the mean length of the orthogonal projection of a cell onto an isotropic
bundle of lines) |
| random dihedral angle |
θ |
a dihedral angle selected uniformly at random in a cell (a typical
dihedral angle of a profile cell; dihedral angle is the angle between neighbouring faces
of a cell) |
| average dihedral angle |
Θ |
the mean dihedral angle of a cell |
| number of faces |
nf |
the number of faces of a cell - in normal tessellations, the number of
vertices nv and the number of edges ne are nv
=2(nf -2) and ne =3(nf -2) |
| shape factor f |
f |
defined by formula  (0≤ f≤1;
f=1 for a ball, f→0 for thin plates and long
rods) |
| shape factor g |
g |
defined by formula  (0≤ g≤1;
g=1 for a ball, g→0 for thin plates and long
rods) |
| area |
v' |
the cell area in a planar profile of 3D cell - area of a cell in a planar
induced tessellation |
| perimeter |
s' |
the cell perimeter total edge length of a planar profile of 3D cell -
perimeter of a cell in a planar induced tessellation |
| number of edges |
ne' |
the number of edges of a profile = the number of profile vertices nv' |
| random angle |
θ' |
a random edge angle of a profile - an edge angle selected uniformly at
random in a profile (a typical edge angle of a typical profile) |
| shape factor |
f ' |
defined by formula (0 ≤ f '≤ 1; f '
=1 for a disk, f ' →0 for a thin strip) |
| chord length |
v'' |
cell length in 1D tessellations induced by original 2D or 3D tessellations (chords lengths of 2D or 3D cells) |