| Summary: | The connectivity and inherent frustration of the kagome lattice can produce interesting electronic structures and behaviors in compounds containing this structural motif. Here we report the properties of Pt<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula><i>X</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> (<i>X</i> = In and Tl) that adopt a double-layer kagome net structure related to that of the topologically nontrivial high-temperature ferromagnet Fe<sub>3</sub>Sn<sub>2</sub> and the density wave hosting compound V<sub>3</sub>Sb<sub>2</sub>. We examined the structural and physical properties of single crystal Pt<sub>3</sub>Tl<sub>2</sub> and polycrystalline Pt<sub>3</sub>In<sub>2</sub> using X-ray and neutron diffraction, magnetic susceptibility, heat capacity, and electrical transport measurements, along with density functional theory calculations of the electronic structure. Our calculations show that Fermi levels lie in pseudogaps in the densities of states with several bands contributing to transport, and this is consistent with our Hall effect, magnetic susceptibility, and heat capacity measurements. Although electronic dispersions, characteristic of simple kagome nets with nearest-neighbor hopping, are not clearly seen, likely due to the extended nature of the Pt <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mi>d</mi></mrow></semantics></math></inline-formula> states, we do observe moderately large and non-saturating magnetoresistance values and quantum oscillations in the magnetoresistance and magnetization associated with the kagome nets of Pt.
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