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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > 3D Geometry, Shape and Space > Dodecahedra

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More Dicey Decisions

Stage: 5 Challenge Level: Challenge Level:1

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

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Paper Folding - Models of the Platonic Solids

Stage: 2, 3 and 4

A description of how to make the five Platonic solids out of paper.

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The Dodecahedron

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Stage: 4 Challenge Level: Challenge Level:1

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.

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Classifying Solids Using Angle Deficiency

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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The Dodecahedron Explained

Stage: 5

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?

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Icosian Game

Stage: 3 Challenge Level: Challenge Level:1

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.

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Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Platonic Planet

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?