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RESISTOR NETWORKS BASED ON POLYHEDRA WITH A FOCUS ON ANTI-PRISMS**

Abstract

The resistance of a network can generally be determined by the equivalent resistance equations; however, these equations can become unruly when working with large, complex resistor networks. In networks with a high degree of symmetry, such as 3-dimensional polyhedra, the vertices can be partitioned into equivalence classes that greatly simplify the computations. In this study, resistor networks were built in the shape of anti-prisms as well as previously known shapes such as a cube and rhombic dodecahedron. Anti-prisms are two identical polygons aligned with an angular twist with vertices connected by an alternating band of triangles. The equivalent resistance across all possible pairs of vertices were calculated using van Steenwijk’s matrix method and compared to the resistance measured using an ohmmeter. The results were confirmed for the previously known shapes, and accounting for the intrinsic uncertainty of the resistors and the ohmmeter, the measurements for the anti-prisms matched with the calculated values. A generalized process for determining the equivalent resistances across various sets of vertices was found for anti-prisms with base polygons of odd as well as even number of vertices.

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