







A regular tetrahedron 
20170312 

From Jeramie: When we have a regular tetrahedron, is it always true that all the angles of the triangles measure 60 degrees? Answered by Penny Nom. 





The surface area of the tetrahedron 
20120404 

From youssef: how to find the total surface area of the tetrahedron ? Answered by Penny Nom. 





The volume of an irregular tetrahedron 
20120222 

From Brittany: If I am given an irregular tetrahedron with the coordinates of the 4 points how do I find the volume? For example I am asked to find the volume and only given the points A(4,3,5), B(2,1,2), C(0,5,0), and D(2,0,0) can you shown me the working and formular to find the volume? Answered by Robert Dawson. 





The volume of a closed 3D mesh object 
20090910 

From Ozen: I want to calculate the volume of a closed 3D mesh object having a surface made up
triangles. Answered by Robert Dawson. 





A triangular pyramid 
20090206 

From kamran: what would be an example of a triangular pyramid Answered by Stephen La Rocque. 





A truncated tetrahedron 
20090205 

From Brad: If you take a regular tetrahedron and truncate it so you keep the original three 60degree angles around one vertex but the legs originating from it become any three consecutive terms of the Fibonacci series the new base is one triangle of a pentagon.
I want to know the height of the new pyramid relative to its new base and the angles between the base and the other three sides. Answered by Robert Dawson. 





Triangular prisms and pyramids 
20090110 

From KJ: What are some items found in a home or school that could be considered a triangular prism or triangular pyramid? Answered by Robert Dawson and Penny Nom. 





Angles in a regular tetrahedron 
20080807 

From Carla: Hi guys,
A regular tetrahedron has all its edges 8cm in length.
Find the angles which an edge makes with the base.
Thanks.
Carla Answered by Penny Nom. 





An irregular tetrahedron 
20080424 

From RAUL: I am looking an expression for an edge length as function of the other five edge lengths of irregular tetrahedron. Answered by Walter Whiteley. 





Scalar triple product and volume of a general tetrahedron 
20070803 

From Anurag: how do you prove that
volume of tetrahedron= 1/12 times scalar triple product of vectors a,b and c? Answered by Stephen La Rocque. 





An irregular tetrahedron 
20070506 

From Carrie: Assume a tetrahedron (not regular) with vertices A, B, C, O, in which vertex
A is at (0,0,0) in Cartesian space, linesegment AB is the xaxis, and face
ABC defines the xy plane (but no edge is parallel to the yaxis).
Assuming that the xyz coordinates of O are all positive, and given the
lengths of all of the linesegments (AB, BC, AC, AO, BO, CO),
but none of the angles, what is the formula for calculating the
xyz coordinates of O? Answered by Penny Nom. 





Iago the Insect lives on the surface of a regular tetrahedron 
20061229 

From Cassie: Iago the Insect lives on the surface of a regular tetrahedron with edges of length 4 inches. He wants to travel on the surface from the midpoint of one edge to the midpoint of the opposite edge. What is the length of the shortest possible trip for Iago to do this? Two edges in a tetrahedron are opposite if they do not share a common endpoint! Answered by Walter Whiteley. 





The volume of an irregular tetrahedron 
20061206 

From Hai Van: Could you please show me the way to calculate the volume of an irregular tetrahedron Answered by Penny Nom. 





What defines a pyramid? 
20060425 

From Julie and son: My son and I think that a pyramid can have any number of sides, but my son's teacher says a pyramid has just 4 sides (including the base). Who's right? Answered by Stephen La Rocque. 





I want to place four sticks equal distance apart into a tennis ball. 
20051213 

From Bev: I want to place four sticks equal distance apart into a 3 inch tennis ball. The circumference of the ball is 9 inches. Where should I place the sticks and how many inches apart. Answered by Chris Fisher. 





The volume of a tetrahedron 
20040203 

From Joseph:
How do I calculate the volume of a bird tetrahedron. I'm trying to find out to get extra credit. I came with this idea while making a origami tetrahedron.
Joseph
P.S. Do you by any chance have instructions for orig ami figures. If you do, please send me some. Thanks!
Answered by Penny Nom. 





The volume of an irregular tetrahedron 
20031124 

From Peter: How do I calculate the volume of an irregular shaped tetrahedron where: side a = 1.4 m side b = 1.4 m side c = 1.2 m and height = 0.75 m at the junction of sides a and b. Answered by Penny Nom. 





A triangular pyramid 
20010514 

From Kumar: In a Pyramid OABC, all the three sides of the base: a, b, c are known. Also known are the angles between the three sides from the vertex O: Angles AOB, BOC, COA. With this information, is it possible to calculate the lengths of the three sides: OA, OB & OC. Answered by Chris Fisher. 





The bond angles of a tetrahedral polygon 
20010314 

From Nishi: how do i prove (a simply as possible) why the bond angles of a tetrahedral polygon are 109.5 degrees? *i already have two explanations that i don't understand. one is about "theory of dot products" and "vectors" and a hooklike symbol w/ a cosine, and the other has an incomprhensible diagram w/ difficult notation PLEASE BE SIMPLE! thanks sooo much Answered by Harley Weston. 





Triakis 
20010217 

From Anne Grant: I am a grade 8 teacher and have come across the term "Triakis" used with Tetrahedron, octahedron, and hexahedron. What does this term refer to, and what's the difference between a triakis polyhedron and one that is not? I'd also like to know what is meant by the term antiprism, as opposed to prism. Answered by Penny Nom. 





Cannonballs 
19990127 

From Roger King: How many cannonballs can be stacked in a triangular pyramid? Answered by Penny Nom. 





Platonic Solids Surface Area 
19981202 

From Rachel Bidwell: How do you find the surface area of the 5 platonic solids, when they each have a volume of one cubic inch Answered by Harley Weston. 





A tetrahedron inscribed in a cube 
19981118 

From Jane: In analyzing a cube, I would like to find a tetrahedron inscribed in the cube which has none of its faces in the planes of the faces of the cube. I would like to see this tetrahedron outlined in the cube. My name is Jane and my email address is BARSOIAN. I am an elementary education student. Answered by Walter Whiteley. 





Three Spheres 
19970114 

From Alan Schnerch: Three spheres of diameter 2 are placed on a level surface so that each sphere touches the other two. A fourth sphere, also of diameter 2, is placed on top of the other three so that it touches all of the other spheres. The distance from the level surface to the highest point of the top sphere is . . .. Answered by Chris Fisher and Harley Weston. 





What is the volume of a regular tetrahedron? 
19961021 

From Paul Bleier: How does one calculate the volume and the height of a three sided pyramid formed by equilateral triangles? Answered by Bruce Gilligan. 





Volume tetraedre 
19980213 

From Solecki Yannick: j`aimerais savoir s`il existe une formule de calcul simplifie pour trouver le volume du tetraedre en fonction de ses cotes et sans utiliser une expression matricielle. Answered by Chris Fisher. 

