perm filename LABEL.FIG[DOC,LMM]1 blob sn#056035 filedate 1973-07-28 generic text, type T, neo UTF8
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------------------------------------------------------------
Figure 1
The Decalin Skeleton

⊗     ⊗
/ \   / \
/   \ /   \
⊗     ⊗     ⊗
|     |     |
|     |     |
⊗     ⊗     ⊗
\   / \   /
\ /   \ /
⊗     ⊗
------------------------------------------------------------
Figure 2
Three of the 10! numberings of
the Decalin Skeleton.

2     4             7     1             4     2
/ \   / \           / \   / \           / \   / \
/   \ /   \         /   \ /   \         /   \ /   \
1     3     5       2     8     9       5     3     1
|     |     |       |     |     |       |     |     |
|     |     |       |     |     |       |     |     |
10    8     6       3     4     5       6     8     10
\   / \   /         \   / \   /         \   / \   /
\ /   \ /           \ /   \ /           \ /   \ /
9     7             6     10            7     9

(2a)                (2b)                 (2c)
------------------------------------------------------------
Figure 3.
Partially labelled graphs reduce
the equivalencies.

2     4             9     7             4     2
/ \   / \           / \   / \           / \   / \
/   \ /   \         /   \ /   \         /   \ /   \
N1     3     5N     N10    8     6N     N      3     1N
|     |     |       |     |     |       |     |     |
|     |     |       |     |     |       |     |     |
10    8     6       1     3     5       6     8     10
\   / \   /         \   / \   /         \   / \   /
\ /   \ /           \ /   \ /           \ /   \ /
9     7             2     4             7     9

(3a)                 (3b)                (3c)

----------------------------------------------------------
Figure 5,9,Orbits in the Decalin Skeleton
⊗     ⊗
/ \   / \
/   \ /   \
+     &     +
|     |     |
|     |     |
+     &     +
\   / \   /
\ /   \ /
⊗     ⊗

-------------------------------------------------------------
Figure 6
Three Labellings of Decalin with
1 N and 9 C's.

⊗     ⊗             N     ⊗             ⊗     ⊗
/ \   / \           / \   / \           / \   / \
/   \ /   \         /   \ /   \         /   \ /   \
N     ⊗     ⊗       ⊗     ⊗     ⊗       ⊗     N     ⊗
|     |     |       |     |     |       |     |     |
|     |     |       |     |     |       |     |     |
⊗     ⊗     ⊗       ⊗     ⊗     ⊗       ⊗     ⊗     ⊗
\   / \   /         \   / \   /         \   / \   /
\ /   \ /           \ /   \ /           \ /   \ /
⊗     ⊗             ⊗     ⊗             ⊗     ⊗

-------------------------------------------------------------
Figure 7
Labellings with 1 N, 1 S, and 8 C's.
A	B	C

⊗   ⊗		       ⊗   ⊗
/ \ / \		      / \ / \
N   ⊗   ⊗		     N   ⊗   ⊗
7a1  |   |   |		7a1a |   |   |
⊗   ⊗   ⊗		     ⊗   ⊗   ⊗
\ / \ /		      \ / \ /
⊗   ⊗		       ⊗   ⊗

N   ⊗		       N   ⊗
/ \ / \		      / \ / \
⊗   ⊗   ⊗		     ⊗   ⊗   ⊗
7a2  |   |   |		7a2  |   |   |		this diagram
⊗   ⊗   ⊗		     ⊗   ⊗   ⊗		is not complete
\ / \ /		      \ / \ /
⊗   ⊗		       ⊗   ⊗

⊗   ⊗		       ⊗   ⊗
/ \ / \		      / \ / \
⊗   N   ⊗		     ⊗   N   ⊗
7a3  |   |   |		7a3  |   |   |
⊗   ⊗   ⊗		     ⊗   ⊗   ⊗
\ / \ /		      \ / \ /
⊗   ⊗		       ⊗   ⊗
-------------------------------------------------------------
Figure 8
1 N to orbit {1,5,6,10}

⊗     ⊗
/ \   / \
/   \ /   \
N     ⊗     ⊗
|     |     |
|     |     |
⊗     ⊗     ⊗
\   / \   /
\ /   \ /
⊗     ⊗

------------------------------------------------------------
Figure 9
Second step of case 5

N   ⊗		       ⊗   N
/ \ / \		      / \ / \
N   ⊗   ⊗		     N   ⊗   ⊗
9a   |   |   |		9b   |   |   |
⊗   ⊗   ⊗		     ⊗   ⊗   ⊗
\ / \ /		      \ / \ /
⊗   ⊗		       ⊗   ⊗

⊗   ⊗		       ⊗   ⊗
/ \ / \		      / \ / \
N   ⊗   ⊗		     N   ⊗   ⊗
9c   |   |   |		9d   |   |   |
⊗   ⊗   ⊗		     ⊗   ⊗   ⊗
\ / \ /		      \ / \ /
⊗   N		       N   ⊗

------------------------------------------------------------
FIGURE 11

C↓6N↓6O↓4S↓4                          The pot of atoms

Taking combinations of
6 atoms

e.g. C↓4S↓2                       76 combinations possible
65 are valid for D.A. Rings

Labelling Step

C        C        C        C           4 Rings generated
/   \    /   \    /   \    /   \         from the example
C     S  C     C  C     S  C     C        C4S2
|     |  |     |  |     |  |     |
C     S  C     S  C     C  C     C
\   /     \  /    \   /     \  /
C        S        S        S

A total of 1176 rings generated from all the
65 combinations of 6 atoms taken from C6N6O4S4

------------------------------------------------------------
1         =C,C,O,O.
/   \
C       2
"       |
C       3            (Fig. 12)
\   /
4

Group is i,r, where
(1 2 3 4) = i
(4 3 2 1) = r

orbits A1 = (1 4)
A2 = (2 3)

Case    Assignment to orbit A1     Remaining Labels
1     C C                        S S
2     C S                        C S
3     S S                        C C

Case 1  C,C --> (1 4)
then S,S --> (2 3)    1 Labelling
(C S S C)
Case 2  C,S --> (1 4)
C --> 1
S --> 4
reduced group is i
C,S --> 2 3          2 labellings
C --> 2 & S --> 3    (C C S S)
S --> 2 & C --> 3    (C S C S)

Case 3     S,S --> (1 4)            1 labelling
then C,C --> (2 3)     (S C C S)
Total of 4 possible labellings.
-----------------------------------------------------------
1
Octahedral
Skeletal        6         2
Framework
5         3

4

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