# Geometric products

The *geometric product* is the fundamental product of geometric algebra. There are two products with symmetric properties called the geometric product and geometric antiproduct.

## Geometric Product

The following Cayley table shows the geometric products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric product is the scalar basis element $$\mathbf 1$$.

Cells colored yellow correspond to the contribution from the wedge product, and cells colored orange correspond to the contribution from the dot product.

## Geometric Antiproduct

The following Cayley table shows the geometric antiproducts between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric antiproduct is the antiscalar basis element $${\large\unicode{x1D7D9}}$$.

Cells colored yellow correspond to the contribution from the antiwedge product, and cells colored orange correspond to the contribution from the antidot product.