Tetrahedron: Quiz

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

Question 2:
Which of the following titles did Tetrahedron have?
 Tetrahedron Hell Looks a Lot Like L.A. How's My Driving, Doug Hastings? Kehoe

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.
Altitude (triangle)Nine-point circleOrthocentric systemCircumscribed circle

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.
TetrahedronSimplexTriangleCentroid

Question 5: A corollary of the usual ________ is that in a tetrahedron with vertices O, A, B, C, we have
Law of cosinesMathematics in medieval IslamHistory of trigonometryLaw of sines

Question 6: The regular tetrahedron has 24 isometries, forming the ________ Td, isomorphic to S4.
Group (mathematics)Dihedral groupGroup actionSymmetry group

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

Question 8: T, isomorphic to ________ A4 (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):
Group theoryAlternating groupGroup (mathematics)Mathieu group

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).
CubeIcosahedronOctahedronDodecahedron

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