  Electronic and topological properties of materials are derived from the
interplay between crystalline symmetry and dimensionality. Simultaneously
introducing 'forbidden' symmetries via quasiperiodic ordering with
low-dimensionality into a material system promises the emergence of new
physical phenomena. Here, we isolate a two-dimensional chalcogenide
quasicrystal and approximant, and investigate associated electronic and
topological properties. Ultra-thin two-dimensional layers of the materials with
a composition close to Ta1.6Te, derived from a layered transition metal
dichalcogenide, are isolated with standard exfoliation techniques and
investigated with electron diffraction and atomic-resolution scanning
transmission electron microscopy. Density functional theory calculations and
symmetry analysis of the large unit-cell crystalline approximant of the
quasicrystal Ta21Te13 reveal the presence of symmetry protected nodal crossings
in the quasicrystalline and approximate phases whose presence is tunable by
layer number. Our study provides a platform for the exploration of physics in
quasicrystalline low-dimensional materials and the interconnected nature of
topology, dimensionality and symmetry in electronic systems.
