Abstract
This paper aims to show that there exists a triangulation of the Heisenberg group mathbb {H}^n into singular simplexes with regularity properties on both the low-dimensional and high-dimensional layers. For low dimensions, we request our simplexes to be horizontal while, for high dimensions, we define a notion of straight simplexes using exponential and logarithmic maps, and we require our simplexes to have high-dimensional straight layers. A triangulation with such simplexes is first constructed on a general polyhedral structure and then extended to the whole Heisenberg group. In this paper, we also provide some explicit examples of grid and triangulations.
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