I have made a solid and would like to know its' name, volume and related formulas. It is made using a flat potato chip bag. The end opposite the factory seal is sealed perpendicular to the factory seal.
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2$\begingroup$ If your object looks like this with the two black lines being the seals and the four red lines being the other edges, then it is a tetrahedron. If its faces are four congruent isosceles triangles then one name for it is a "tetragonal_disphenoid" $\endgroup$– HenryCommented Feb 2 at 23:39
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1$\begingroup$ @JosephO'Rourke If your "isoscelest tetrahedron" was a typo for "isosceles tetrahedron" then apparently that can also be used for something else where opposite edges are equal so each triangle is congruent but there is no need for isosceles triangles. $\endgroup$– HenryCommented Feb 2 at 23:50
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1$\begingroup$ @Tom Please note that one might make a case that this question was not exactly on-topic for MathOverflow (which is intended for questions that arise in the course of original mathematics research), and subsequent questions should probably be directed at math.stackexchange.com In this instance people have thoughtfully engaged and found the answer, but I just wanted you to be aware that this seems to have been a corner case. The question currently has three votes to close, don't take it personally if that ends up happening. Best of luck and enjoy the maths you are investigating! $\endgroup$– David Roberts ♦Commented Feb 3 at 0:45
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1$\begingroup$ Thank you. math.stackexchange.com will be my go to in the future. I have my answer and as far as I'm concerned the question is closed. Thanks to All $\endgroup$– Tom LechnerCommented Feb 3 at 1:10
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1$\begingroup$ @Tom just so you know, giving Henry's answer the tick will help the software know the question is resolved. $\endgroup$– David Roberts ♦Commented Feb 3 at 2:51
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1 Answer
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Just for completeness as requested in the comments, if your object looks like this
with the two black lines being the seals and the four red lines being the other edges, then it is a tetrahedron though not a regular tetrahedron.
If its faces are four congruent isosceles triangles then one name for it is a "tetragonal_disphenoid" and another "digonal antiprism". That would be a special case of an "isosceles tetrahedron" where opposite edges are equal so each triangle is congruent (though there is no need for isosceles triangles).
As you have seen from that last link to Wolfram Mathword, if the three pair of opposite sides have lengths $a,b,c$ (perhaps here $b=c$) then the volume is $$V=\sqrt{\dfrac{(a^2+b^2-c^2)(b^2+c^2-a^2)(c^2+a^2-b^2)}{72}}.$$
As David Roberts has commented, this level of question may be more appropriate for math.stackexchange.com than Mathoverflow.net.
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$\begingroup$ Excellent. As an outsider, I must ask, were the other answers wrong or just above my understanding? I will continue to follow and hopefully not comment further until removed. $\endgroup$ Commented Feb 4 at 20:02