# 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;