# This worksheet calculates various graphs that are needed for the
# globally rigid calculations.  The first one is K[5,5] with one
# Hennenberg edge split performed on the edge {5,6} with the new vertex
# 11 being joined to 1,2,5,6.
> with(networks):
> G:=complete(5,5):
> delete(edges({5,6},G),G):
> addvertex({11},G):
> addedge({{11,5},{11,6},{11,3},{11,4}},G);
                       e26, e27, e28, e29
> ends(G);
{{1, 8}, {2, 6}, {3, 6}, {3, 7}, {3, 9}, {4, 7}, {4, 8}, {4, 10}, {5, 8}, 

  {5, 11}, {6, 11}, {1, 6}, {2, 8}, {3, 10}, {5, 9}, {1, 7}, {1, 9}, {1, 10}, 

  {2, 7}, {2, 9}, {2, 10}, {3, 8}, {4, 6}, {4, 9}, {5, 7}, {5, 10}, {3, 11}, 

  {4, 11}}
> draw(G);

# The following is the cone on K[5,5] used for calculations in 4-space.
> with(networks):
> G:=complete(5,5):
> delete(edges({5,6},G),G): delete(edges({4,7},G),G):
> addvertex({11},G):
> addedge({{11,4},{11,5},{11,6},{11,7},{11,8}},G);
                    e26, e27, e28, e29, e30
> draw(G);

# The following is the X replacement on K[5,5] used for calculations in
# 3-space.
> with(networks):
> G:=complete(5,5):
> addvertex({11},G):
> addedge({seq({i,11},i=1..10)},G);
        e26, e27, e28, e29, e30, e31, e32, e33, e34, e35

# The following is the construction of a two isostatic graphs joined by
# 7 disjoint bars. 
> with(networks):
> G:=void(14):
> addedge(ends(complete({1,2,3,4})),G):
> addedge(ends(complete({8,9,10,11})),G):
> addedge({{5,2},{5,3},{5,4},{6,1},{6,3},{6,4},{7,1},{7,2},{7,4}},G):
> addedge({{12,8},{12,9},{12,10},{13,8},{13,10},{13,11},{14,8},{14,9},{1
> 4,11}},G):
> addedge({{1,8},{2,9},{3,10},{4,11},{5,12},{6,13},{7,14}},G):
> draw(G);

> nops(ends(G));
                               37
> restart;