  We propose a realization of the lattice symmetry assisted second order
topological superconductors with corner Majorana zero modes (MZM) based on
two-dimensional topological insulators (2DTI). The lattice symmetry can
naturally lead to the anisotropic coupling of edge states along different
directions to the in-plane magnetic field and conventional s-wave pairings,
thus leading to a single MZM locating at the corners for various lattice
patterns. In particular, we focus on the 2DTI with D$_{3d}$ lattice symmetry
and found different types of gap opening for the edge states along the armchair
and zigzag edges in a broad range of parameters. As a consequence, a single MZM
exists at the corner between the zigzag and armchair edges, and is robust
against weakly lattice symmetry broken. We propose to realize such corner MZMs
in a variety of polygon patterns, such as triangles and quadrilaterals. We
further show their potentials in building the Majorana network through
constructing the Majorana Y-junction under an in-plane magnetic field.
