Icosahedron Fractal

A double tower of icosahedra is aligned along each edge of a larger enveloping icosahedron. A tower stacks gradually diminishing icosahedra on the face of an icosahedron. The rate of reduction is 1/2, and each tower could theoretically have an infinite number of icosahedra converging to a vertex of the enveloping icosahedron. Each icosahedron in the assembly could be replaced with a fractal icosahedron to form an infinite fractal structure.



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


This Demonstration can serve as a reminder of certain geometrical features—for instance, that the icosahedron has 56 edges, corresponding to the number of faces of the rhombic triacontahedron, and that the arrangement of 16 edges corresponds to the faces of the cube. The assembly is a good illustration of the self-similarity property of fractals. It also shows a geometrical example of how an infinite set of volumes can have a finite boundary. Related schoolroom exercises could include the calculation of the height of a tower, the volume of a tower, and the proportions of icosahedra.
    • 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 © 2017 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+