Introducing Disphenoid
A disphenoid is a non-regular tetrahedron whose faces have the same perimeter/area, and thus consist of congruent triangles.
For a disphenoid with edge lengths to exist, the value of must strictly be greater than...
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The answer is 3.
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1 solution
The formula for the volume V of disphenoid given its edge lengths a , b , and c is:
V = 7 2 ( a 2 + b 2 − c 2 ) ( a 2 − b 2 + c 2 ) ( − a 2 + b 2 + c 2 )
Substituting for values in terms of x, we get
V = 7 2 ( x 2 + 2 x + 3 ) ( x + 5 ) ( x − 3 ) ( x + 1 ) 2
It will be clear from here when V becomes imaginary, when it becomes zero, and when it becomes a positive real number. :)