Cartesian coordinates and simplicial coordinates
Cartesian coordinates use a set of mutually orthogonal unit
basis vectors to span a space. In the photo to the right,
the familiar 3‑D Cartesian unit vectors
ı⃗,
ȷ⃗,
k⃗ are modeled with toothpicks
stuck into a styrofoam origin. These vectors satisfy the definition of a
basis
for 3‑space:
