Heronian Rotational Mandala: Exact Lattice Tessellations and Artistic Mandalas from the 13–14–15 Triangle

This preprint revisits the Heronian rotational mandala built from the classical 13–14–15 triangle.

On the one hand, the paper develops an exact geometric construction: a lattice tessellation based on the 13–14–15 triangle and its reflected / excentral variants, together with precise rotational patterns (of order 12) that can be stated and proved rigorously. This is the “hard” mathematical core of the work.

On the other hand, some of the most colourful figures in the paper are deliberately adjusted as mathematical art. In these images, the exact lattice is used as a starting point, but small visual modifications are introduced to enhance symmetry, colour and global aesthetics. These artistic mandalas are not intended as strict proofs of exact tessellations, but as illustrations and extensions of the underlying structure.

This Version 2 adds an explicit clarifying note at the beginning of the manuscript to make this distinction fully transparent: which parts correspond to exact, verifiable constructions, and which figures should be understood as artistic interpretations inspired by the same geometry.