  This paper provides a simple, compact and efficient 90-line pedagogical
MATLAB code for topology optimization using hexagonal elements (honeycomb
tessellation). Hexagonal elements provide nonsingular connectivity between two
juxtaposed elements and, thus, subdue checkerboard patterns and point
connections inherently from the optimized designs. A novel approach to generate
honeycomb tessellation is proposed. The element connectivity matrix and
corresponding nodal coordinates array are determined in 5 (7) and 4 (6) lines,
respectively. Two additional lines for the meshgrid generation are required for
an even number of elements in the vertical direction. The code takes a fraction
of a second to generate meshgrid information for the millions of hexagonal
elements. Wachspress shape functions are employed for the finite element
analysis, and compliance minimization is performed using the optimality
criteria method. The provided Matlab code and its extensions are explained in
detail. Options to run the optimization with and without filtering techniques
are provided. Steps to include different boundary conditions, multiple load
cases, active and passive regions, and a Heaviside projection filter are also
discussed. The code is provided in Appendix~A, and it can also be downloaded
along with supplementary materials from
\url{https://github.com/PrabhatIn/HoneyTop90}.
