Polyhedra

  • Face Painting
    problem

    Face Painting

    Age
    7 to 11
    Challenge level
    You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.
  • Dodecamagic
    problem

    Dodecamagic

    Age
    7 to 11
    Challenge level

    Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

  • Child's Play
    problem

    Child's Play

    Age
    7 to 11
    Challenge level

    A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

  • A Chain of Eight Polyhedra
    problem

    A Chain of Eight Polyhedra

    Age
    7 to 11
    Challenge level

    Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

  • Tetrahedron faces
    problem

    Tetrahedron Faces

    Age
    7 to 11
    Challenge level
    One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
  • Redblue
    problem

    Redblue

    Age
    7 to 11
    Challenge level

    Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

  • Icosian Game
    problem

    Icosian Game

    Age
    11 to 14
    Challenge level

    This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

  • Classifying Solids using Angle Deficiency
    problem

    Classifying Solids Using Angle Deficiency

    Age
    11 to 16
    Challenge level

    Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

  • Dodecawhat
    problem

    Dodecawhat

    Age
    14 to 16
    Challenge level

    Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

  • Proximity
    problem

    Proximity

    Age
    14 to 16
    Challenge level

    We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

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