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How many faces?


Best Answer plasmid, 09 April 2013 - 04:47 AM

The shortest and most intuitive (although least formal) proof of the answer that I can come up with.

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Go to the full post


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9 replies to this topic

#1 bonanova

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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?


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 ThunderCloud

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Posted 07 April 2013 - 11:59 PM

Spoiler for If I am picturing this right...


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#3 nakulendu

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Posted 08 April 2013 - 04:21 AM

Spoiler for Maybe


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#4 bonanova

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Posted 08 April 2013 - 06:00 AM

No correct answers yet.


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#5 Yodell

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Posted 08 April 2013 - 11:32 AM

I'm guessing

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#6 k-man

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Posted 08 April 2013 - 03:37 PM

Spoiler for you get a...


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#7 BobbyGo

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Posted 08 April 2013 - 03:52 PM

Spoiler for a guess


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#8 BobbyGo

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Posted 08 April 2013 - 05:32 PM

Spoiler for a guess

 

Too late to edit:

Spoiler for Correction

Edited by BobbyGo, 08 April 2013 - 05:33 PM.

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#9 plasmid

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Posted 09 April 2013 - 04:47 AM   Best Answer

The shortest and most intuitive (although least formal) proof of the answer that I can come up with.

Spoiler for

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#10 bonanova

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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.

Spoiler for

 

plasmid: Bingo.

 

Spoiler for Plasmids proof


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