Abstract
The paper proposes a method of forming geometric networks of one arch radius using regular spherical polyhedrons. A variant of network placing on a spherical icosahedron and, accordingly, on a sphere is proposed. The placement on the sphere of arches of one radius differs from the placement of meridians and is an effective solution for network with a smallest size of arch segments, with nodes of two intersecting arches formed on circles of the same radius and on regular spherical polyhedrons. The problem is solved by constructing an arches of the same radius using paired circles with two standard arch sizes. Several variants of the twin geodetic domes with the given stability loss are suggested.
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