Tree in Polyhedron Figures
Find a tree in the polyhedron of figure 1.3 which contains all the vertices. Construct the dual graph Г and show that Г contains loops. (You don't have to construct the graph, but please describe it to me how it looks like.) (SEE ATTACHMENT)
© BrainMass Inc. brainmass.com December 24, 2021, 5:09 pm ad1c9bdddfhttps://brainmass.com/math/geometry-and-topology/tree-polyhedron-figures-31907
Solution Preview
Please see attached file
4. Find a tree in the polyhedron of figure 1.3 which contains all the vertices. Construct the dual graph Г and show that Г contains loops. (You don't have to construct the graph, but please describe it to me how it looks like.)
5. Having done Problem 4, thicken both T and Г in the polyhedron. T is a tree, so thickening it gives a disc. What do you obtain when you thicken Г?
8. Check that v - e + f = 0 for the polyhedron shown in Fig. 1.3. Find a polyhedron which can be deformed into a double-torus(two torus are stuck together) and calculate its Euler ...
Solution Summary
A tree in polyhedron figures are determined.