We have investigated the structural chemistry, magnetic and electrical transport properties of the ternary compounds ${R}_{20}{\mathrm{Ni}}_{42}{\mathrm{As}}_{31}$ $(R=\mathrm{La},$ Ce, Pr, Nd, Sm) crystallizing in the hexagonal ${\mathrm{Sm}}_{20}{\mathrm{Ni}}_{42}{\mathrm{P}}_{31}$-type structure, which has been determined from single-crystal x-ray data of the Ce-containing compound: space group ${P6}_{3}/m,$ $a=2.1148(1),$$c=0.40331(5)\mathrm{nm},$${R}_{F}=0.051$ for 304 structure factors and 47 variable parameters. These arsenides belong to a large structural family with a metal to metalloid ratio of 2:1. The magnetic properties are as follows: ${\mathrm{La}}_{20}{\mathrm{Ni}}_{42}{\mathrm{As}}_{31}$ is a Pauli-type paramagnet above 1.8 K, ${\mathrm{Pr}}_{20}{\mathrm{Ni}}_{42}{\mathrm{As}}_{31}$ orders antiferromagnetically at ${T}_{N}=11\mathrm{K}$ and shows a metamagnetic transition above $B=0.3\mathrm{T},$ ${\mathrm{Nd}}_{20}{\mathrm{Ni}}_{42}{\mathrm{As}}_{31}$ and ${\mathrm{Sm}}_{20}{\mathrm{Ni}}_{42}{\mathrm{As}}_{31}$ undergo ferromagnetic ordering at ${T}_{C}=28\mathrm{K}$ and 10 K, respectively. ${\mathrm{Ce}}_{20}{\mathrm{Ni}}_{42}{\mathrm{As}}_{31}$ reveals a strong deflection of the linear temperature dependence of the inverse susceptibility due to an intermediate valence behavior. The temperature dependence of the electrical resistivities for the La, Pr, Nd, Sm containing samples corroborates with the metallic state of the nonmagnetic (La) and the magnetically ordered compounds, whereas in case of ${\mathrm{Ce}}_{20}{\mathrm{Ni}}_{42}{\mathrm{As}}_{31}$ the resistivity seems to be determined by an interplay of Kondo scattering and crystalline field effects. ${L}_{\mathrm{III}}$ x-ray absorption spectra confirm the demagnetization effects owing to valence fluctuations, the actual valence thereby changes from $v=3.05$ at room temperature to 3.11 at 10 K.