Term to describe the two ways of labeling the vertices of a tetrahedron.

Question

I can label the vertices of a tetrahedron in two different ways as are depicted in the following picture. How to differentiate the two? Is there a term or a mathematical statement? I suspect that it is "chirality" but I'm not sure.

In this context, the order of labeling is significant. In the picture, $A$ is between plane $BCD$ and the eyes of a typical StackExchange user.

Answer 1

If you order the vertices $A$, $B$, $C$, $D$, then there's some evidence that (b) could be called "positively oriented" (or perhaps "right chiral") and (a) could be called "negatively oriented" (or perhaps "left chiral"). The reason is an analogy to the positive orientation of the standard coordinate system: we should take the tetrahedron with vertices $(0,0,0)$, $(1,0,0)$, $(0,1,0)$, $(0,0,1)$ to have positive orientation.