On 3/19/07, Ralph Shumaker <[EMAIL PROTECTED]> wrote:
Andrew Lentvorski wrote:
> Ralph Shumaker wrote:
>
>> Apparently, the two pyramids in question are *not* the same, except
>> that they are both completely equilateral. One has a square base.
>> The other has a triangle base. The answer seems like it would be 7
>> since the one has 5 sides, the other has 4 sides, and one side of
>> each is completely covered up. But 7 is *not* the correct answer.
>> Can you guess what it is? (BTW, the official SAT answer apparrently
>> *was* "7", but was challenged, and found to be wrong.)
>
>
> The trick has to do with the dihedral angles:
>
> Tetrahedron = 70.53
> Octahedron = 109.47 (if you split it in half it's the second pyramid)
>
> 109.47+70.53 = 180.00
>
> -a
>
... which gives you how many sides left exposed? (Bonus points: Name
the shapes of each side and the number of each shape (somebody other
than Andrew :-) since he apparrently has it).)
I get 5 faces. A square, two equilateral triangles, and two rhombuses
(rhombi?) with 60-degree and 120-degree internal angles. The trick is
that there are two faces which are composed of pairs of coplanar
equilateral triangles that merge into a rhombus.
Had to get out my dusty stick-and-connector geometric modeling kit to be sure.
carl
--
carl lowenstein marine physical lab u.c. san diego
[EMAIL PROTECTED]
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