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Figure 1. The various properties of a plane.

In the 5D conformal geometric algebra $$\mathcal G_{4,1}$$, a plane $$\mathbf g$$ is a quadrivector having the general form

$$\mathbf g = g_x \mathbf e_{4235} + g_y \mathbf e_{4315} + g_z \mathbf e_{4125} + g_w \mathbf e_{3215}$$ .

A plane can be viewed as an infinitely large sphere containing the point at infinity. A plane in conformal geometric algebra is the precise analog of a plane in rigid geometric algebra, with the only difference being that the representation of a plane in the conformal model contains an additional factor of $$\mathbf e_5$$ in each term.

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