  We give explicit formulae for a differential graded Lie algebra (DGLA) model
of the triangle which is symmetric under the geometric symmetries of the cell.
This follows the work of Lawrence-Sullivan on the (unique) DGLA model of the
interval and of Gadish-Griniasty-Lawrence on an explicit symmetric model of the
bi-gon. As in the case of the bi-gon, the essential intermediate step is the
construction of a symmetric point. Although in this warped geometry of points
given by solutions of the Maurer-Cartan equation and lines given by a gauge
transformation by Lie algebra elements of grading zero, the medians of a
triangle are not concurrent, various other geometric constructions can be
carried out. The construction can similarly be applied to give symmetric model
of arbitrary $k$-gons.
