Exact Coordinates of Golden Rhombic Solids

This Demonstration gives exact coordinates of various golden rhombic solids. Using three golden rectangles, the coordinates of the vertices of the regular icosahedron are , , or , where is the golden ratio. The coordinates of all of the golden rhombic solids are constructed by adding vectors, so their coordinates are of the form , where and are integers.
The prolate rhombohedron is constructed using the origin and the vertices on one face of the icosahedron as its first four vertices. Twenty rhombohedra constructed in this way form the hexecontahedron, and the other solids are built up from there.



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


The data format for polyhedra as {faces, vertex coordinates} was introduced in [1].
[1] R. E. Maeder, The Mathematica Programmer II, New York: Academic Press, 1996.
    • 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.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+