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: , that is, .


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


This rhombohedron could be considered as a building block in structures where rhombi with diagonal ratios or occur. The rhombic enneacontahedron is an example of a rhombus and a rhombus; the rhombic dodecahedron is a rhombus and the median rhombic triacontahedron is a rhombus.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.