Polyhedra

There are 45 NRICH Mathematical resources connected to Polyhedra
Rhombicubocts
problem

Rhombicubocts

Age
11 to 14
Challenge level
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Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?
Magnetic personality
problem

Magnetic personality

Age
7 to 16
Challenge level
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60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Child's Play
problem

Child's play

Age
7 to 11
Challenge level
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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?
Lighting up time
problem

Lighting up time

Age
7 to 14
Challenge level
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A very mathematical light - what can you see?
Icosian Game
problem

Icosian game

Age
11 to 14
Challenge level
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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.

Proximity
problem

Proximity

Age
14 to 16
Challenge level
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We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
Platonic Planet
problem

Platonic planet

Age
14 to 16
Challenge level
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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?
More Dicey Decisions
problem

More dicey decisions

Age
16 to 18
Challenge level
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The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?
Dodecawhat
problem

Dodecawhat

Age
14 to 16
Challenge level
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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.