What is a Tetrahedron?

Question

What is a Tetrahedron?

Answer 1

A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids.

The tetrahedron is one kind of pyramid, the second most common type; a pyramid has a flat base, and triangular faces above it, but the base can be of any polygonal shape, not just square or triangular.

Answer 2

http://en.wikipedia.org/wiki/Tetrahedron

Answer 3

regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids.

The tetrahedron is one kind of pyramid, the second most common type; a pyramid has a flat base, and triangular faces above it, but the base can be of any polygonal shape, not just square or triangular.

http://kjmaclean.com/Geometry/Tetrahedro...

Answer 4

a four sided object looks similar to pyramid, all the sides are triangles

Answer 5

A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids.

The tetrahedron is one kind of pyramid, the second most common type; a pyramid has a flat base, and triangular faces above it, but the base can be of any polygonal shape, not just square or triangular.

http://en.wikipedia.org/wiki/Tetrahedron

Answer 6

Tetrahedron as the name implies is a four faced solid. It's the only (we talk of only regular solids) Platonic solid that is self-dual (its dual also is a Tetrahedron); the other 4 occur as two dual pairs (Octahedron-Cube, Dodechedron-Icosahedron). It is also the first of the class of 'Pyramids', of triangular base. But unlike other pyramids, it is symmetrical - you can make any face as base.

Tetrahedron has 4 vertices, each of which is connected to all other vertices. I call it a 'minimal' figure (here it is 'minimal' figure of 3dim); its Next Higher Dimensional Constituent (NHDC) is also a 'minimal' figure (of 2dim) that is 'equilateral' triangle, as every vertex of it is connected to other vertices. If coordinates of vertices ([x0, y0, z0], [x1, y1, z1], [x2, y2, z2], [x3, y3, z3]) are known, it is the easiest to compute volume (V) =

|x0 y0 z0 1|

|x1 y1 z1 1| X(1/3!).

|x2 y2 z2 1|

|x3 y3 z3 1|

By extrapolating Tetrahedron to the 4th dimension by induction, its 4dim counterpart can be described.