Vertex Arrangement - Edge Arrangement

Polyhedra can also share an edge arrangement while differing in their faces.

For example, the self-intersecting great dodecahedron shares its edge arrangement with the convex icosahedron:

Two polyhedra with same edge arrangement.

icosahedron
(20 triangles)
great dodecahedron
(12 intersecting pentagons)

Read more about this topic:  Vertex Arrangement

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