Polyhedra

  • Tetrahedra Tester
    problem

    Tetrahedra Tester

    Age
    14 to 16
    Challenge level

    An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

  • Platonic Planet
    problem

    Platonic Planet

    Age
    14 to 16
    Challenge level
    Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?
  • Tetra Inequalities
    problem

    Tetra Inequalities

    Age
    16 to 18
    Challenge level

    Can you prove that in every tetrahedron there is a vertex where the three edges meeting at that vertex have lengths which could be the sides of a triangle?

  • More Dicey Decisions
    problem

    More Dicey Decisions

    Age
    16 to 18
    Challenge level

    The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

  • The Dodecahedron
    problem

    The Dodecahedron

    Age
    16 to 18
    Challenge level

    What are the shortest distances between the centres of opposite faces of a regular solid dodecahedron on the surface and through the middle of the dodecahedron?

  • The Dodecahedron Explained
    article

    The Dodecahedron Explained

    What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?
  • Platonic and Archimedean Solids
    page

    Platonic and Archimedean Solids

    In a recent workshop, students made these solids. Can you think of reasons why I might have grouped the solids in the way I have before taking the pictures?

  • Modular origami polyhedra
    page

    Modular Origami Polyhedra

    These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

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