Chemistry Reference
In-Depth Information
Fig. 6.5
The molecular graph
ofaC
4
C
8
(R) nanotube
Fig. 6.6
The 2D lattice of a
C
4
C
8
(R) nanotube
Fig. 6.7
The molecular graph
ofaC
4
C
8
(S) nanotube
leapfrog operation, Figs.
6.5
and
6.6
.AC
4
C
8
(R) nanotube is another beautiful math-
ematical object constructed by squares and octagons. An charming example is shown
in Figs.
6.7
and
6.8
.A
carbon nanotorus
is geometrically obtained by connecting
the two ends of a carbon nanotube into a ring, Figs.
6.9
,
6.10
,
6.11
and
6.12
.
The symmetry properties of these nanostructures are one of the main subject of
this study.
Suppose (
G
,
H
is the set of
all
ordered pairs
(
a, b
) where
a
∈
G
and
b
∈
H
, together with the following group
·
1
) and (
H
,
·
2
) are groups. The
cartesian product G
×
