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How many faces?
Posted 07 April 2013 - 11:28 PM
A regular tetrahedron (a solid with four faces) can be constructed from four unit-sided equilateral triangles.
Four similar triangles can also be assembled to have a common vertex and a unit-square base.
Adding that square creates a square pyramid (with five faces.)
These two solids can now be joined into another solid: by gluing together, vertex to vertex,
a triangular face from each of them.
How many faces does the joined solid have?
Vidi vici veni.
Posted 08 April 2013 - 05:32 PM
Spoiler for a guess
Too late to edit:
Edited by BobbyGo, 08 April 2013 - 05:33 PM.
Posted 09 April 2013 - 04:47 AM Best Answer
Posted 09 April 2013 - 11:15 AM
The shortest and most intuitive (although least formal) proof of the answer that I can come up with.
Vidi vici veni.
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