Here we discuss, based on first-principles calculations, two-dimensional (2D) kagome lattices composed of polymerized heterotriangulene units, planar molecules with D _3h point group containing a B, C, or N center atom and CH ₂ , O, or CO bridges. We explore the design principles for a functional lattice made of 2D polymers, which involves control of π-conjugation and electronic structure of the knots. The former is achieved by the chemical potential of the bridge groups, while the latter is controlled by the heteroatom. The resulting 2D kagome polymers have a characteristic electronic structure with a Dirac band sandwiched by two flat bands and are either Dirac semimetals (C center), or single-band semiconductors - materials with either exclusively electrons (B center) or holes (N center) as charge carriers of very high mobility, reaching values of up to ∼8 × 10 ³ cm ² V ^-1 s ^-1 , which is comparable to crystalline silicon.