In 1980 the Educational Testing Service offered this question on an aptitude test:
In pyramids ABCD and EFGHI shown above, all faces except base FGHI are equilateral triangles of equal size. If face ABC were placed on face EFG so that the vertices of the triangles coincide, how many exposed faces would the resulting solid have?
(A) Five (B) Six (C) Seven (D) Eight (E) Nine
Which is correct?
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The test makers were expecting the answer (C), but several students pointed out that in fact (A) is correct — the shapes fit together to produce a surprisingly simple object with only five faces.
This is easiest to see if you imagine two square pyramids side by side: The tetrahedron fits precisely between them to make a smooth-sided “pup tent”:
If you have polyhedral dice, try fitting the face of a 4-sided to an 8-sided die; you’ll find that the adjoining sides are coplanar.
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