Pyramids: two perpendicular lateral face and are equilateral triangle

pynam

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Can we have a triangular pyramid in which two lateral faces are perpendicular, and also these lateral faces (triangles) are equilateral? If not, why not?
 
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Dr.Peterson

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Can we have a pyramid in which two lateral faces are perpendicular, and also these lateral faces (triangles) are equilateral? If not, why not?
Imagine taking two equilateral triangles and gluing then together at right angles. Can you complete this to make a pyramid?

You may have to tell me how you are defining "pyramid", because the word is sometimes used in a restricted way (e.g. right regular pyramid) rather than its most general sense.
 

pynam

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Imagine taking two equilateral triangles and gluing then together at right angles. Can you complete this to make a pyramid?

You may have to tell me how you are defining "pyramid", because the word is sometimes used in a restricted way (e.g. right regular pyramid) rather than its most general sense.
I'm referring to any triangular pyramid, it does not have to be regular pyramid.

Why can't I 'glue' two triangles at right angles, and third triangle (not the base) will have bigger sides to make a pyramid.
 

Dr.Peterson

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I'm referring to any triangular pyramid, it does not have to be regular pyramid.

Why can't I 'glue' two triangles at right angles, and third triangle (not the base) will have bigger sides to make a pyramid.
Are you saying you think you CAN'T do it? Why do you think that?

Or are you agreeing with me that this seems a perfectly reasonable thing to do (and in fact you can do it with some pieces of paper if you wish)?
 
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