# Calculate Squared Rectangles of GreatRhombicosidodecahedralGraph?

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 Hi, I have been calculating the voltage and current through nodes and edges of the edge skeletons of polyhedra. In particular, the Platonic solids and the Archimedean solids. One edge is treated as a direct current 'battery' or EMF, all edges have unit resistance, and using Kirchhoff's Laws of Voltage and Current, all the node voltages and edge currents can be calculated. The graph, labeled with edge currents and flow directions is called a Smith diagram. Once this is done, a 'Squared Rectangle' ( a dissection of a rectangle into squares) can be constructed with the edge currents as the square sizes. Depending on the edge which is chosen for the battery, different Squared Rectangles may result. The Platonic solids have edges which are invariant under symmetry, so only produce one unique squared rectangle. Also the cube and octahedron, when considered as graphs are dual to each other, dual graphs produce the same squared rectangle, same for the icosahedron and dodecahedron. The tetrahedron is of course dual to itself. So from the Platonic solids we can derive only 3 unique squared rectangles. Due to the symmetry of the Platonic solids, some edges have zero currents and so have vanishing zero size squares. With the Archimedean solids, there are 1,2 or 3 different types of edge under symmetry depending on the solid. So quite a few more squared rectangles to discover, many with quite intricate patterns. I had written a C++ program some time ago which used node analysis to generate the squared rectangle 'Bouwkampcode' from the Archimedean solids. Here's a PDF which is the collection of squared rectangles I obtained. I got all except 3 belonging to the GreatRhombicosidodecahedron and it's graph. The double precision overflowed when I tried to calculate it. Recently it occurred to me it might be easier to use the precision, inbuilt data and functions of Mathematica to perform these calculations. I started testing out functions I might use. I tried;  GraphData["GreatRhombicosidodecahedralGraph", "LaplacianMatrix"], but got an error; Missing["TooLarge"] Not sure what the error means, the matrix is large but not massive. I am still finding my way around Mathematica so my question is how do I get around this error? and how do I use mapping of functions to do the Johnson solids as well? Answer Answer