7393
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2011-02-01T00:00:01
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<p>Alison and Steve wish to make a new sort of die which can land on its faces and its corners. <br></br>
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They plan to start with a cube and make planar cuts across the corners to create a solid which, when rolled, has a good chance of landing on the 'corners' and the 'faces'<br></br>
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Consider designing such a die such that it is symmetrical -- i.e. each corner is to be cut off in the same way.<br></br>
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How many faces would the die have and what shape would they each be?<br></br>
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Draw a net of a cube and indicate accurately the lines along which the cuts are to be made.<br></br>
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Where would you align the cuts such that each of the new faces was of the same area?<br></br>
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<span style="font-weight: bold;">Collaboration/cross curricular activity:</span> Suppose that we wish to make a physical die of this sort such that there are equal probabilities of landing on each of the 'faces' and 'corners'. Discuss with DT the possible construction of such a die and plan a way of producing the die.<br></br>
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<p>You'd end up with an truncated cube: there's a picture <a href="http://en.wikipedia.org/wiki/Truncated_cube">here</a>.</p>
<p>It's got six octagonal faces, and 8 faces which are equilateral triangles. To ensure each new triangle has the same area, you should remove an identically sized right-angled triangle from each corner of the square faces. Here's a picture, you should cut along the solid black lines:</p>
<p style="text-align: center;"> <mdo:image alt="Truncated Cube Net" src="Truncated%20cube%20net.png" style="width: 400px; height: 334px;"></mdo:image></p>
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Chopped Dice
Can you make a new type of fair die with 14 faces by shaving the
corners off a cube?
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