Question 1: Regular tetrahedra cannot tessellate space by themselves, although this result seems likely enough that ________ claimed it was possible.  

Question 2: Which of the following titles did Tetrahedron have?



Question 3: The circumsphere of the medial tetrahedron is analogous to the triangle's ________, but does not generally pass through the base points of the altitudes of the reference tetrahedron.  

Question 4: In other words, if C is the ________ of the base, the distance from C to a vertex of the base is twice that from C to the midpoint of an edge of the base.  

Question 5: A corollary of the usual ________ is that in a tetrahedron with vertices O, A, B, C, we have  

Question 6: The regular tetrahedron has 24 isometries, forming the ________ T_{d}, isomorphic to S_{4}.  

Question 7: In ________, a tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex.  

Question 8: T, isomorphic to ________ A_{4} (the identity and 11 proper rotations) with the following conjugacy classes (in parentheses are given the permutations of the vertices, or correspondingly, the faces, and the unit quaternion representation):  

Question 9: The vertices of a ________ can be grouped into two groups of four, each forming a regular tetrahedron (see above, and also animation, showing one of the two tetrahedra in the cube).  

Question 10: A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the ________.  

