Kanoodle Constructions of Regular Polyhedra

A guided research project in Geometry & Dynamics.

← Geometry & Dynamics projects

Experience Research Geometry & Dynamics

Question

Which regular polyhedra can be built from Kanoodle pieces, and what makes the construction possible?

Local choices at each vertex determine whether the pieces can close into a regular solid.
Local choices at each vertex determine whether the pieces can close into a regular solid.

Goals

  • Relate physical constructions to faces, edges, vertices, and symmetry.
  • Build and explain examples of regular polyhedra.

Method

Combine hands-on construction with the combinatorial rules for regular polyhedra.

  • List possible face shapes and vertex arrangements using angle and counting constraints.
  • Design Kanoodle assemblies for the viable cases.
  • Check each model with Euler's formula and compare it with the five Platonic solids.