Rhombohedron with Variable Faces
Rhombohedron with Variable Faces
You can create various rhombohedra by tilting the four parallel edges of a cube or varying the face diagonals. This Demonstration focuses on the special case where the rhombohedron has four faces with diagonal ratio and two faces with diagonal ratio , where is the golden ratio. Let the edge of a cube be . Tilt four parallel edges by degrees, then reduce the diagonal of two faces to . One interesting feature of this polyhedron is that the distance between the two thin rhombi is the golden ratio. The half-diagonals of the thin rhombus are and . This illustrates an interesting relationship: +1=, that is, +1=3.
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