Xerogels, aerogels, cryogels and lyogels based on a polyurethane-polyisocyanurate mixture or a polyurea-polyisocyanurate mixture and having a density of ≤ 250 kg/m 3, wherein the mixture is obtained from a reaction mixture consisting of the following components i) at least one isocyanate-reactive component from the group consisting of polyamines having a number average functionality of from ≥ 2 to ≤ 6.5 and a number average molecular weight of from 100 to 1000 g/mol, polyester polyols having a number average functionality of from ≥ 1.8 to ≤ 6.5 and a hydroxyl number of from 50 to 600 mg KOH/g, polyether ester polyols having a number average functionality of from ≥ 1.8 to ≤ 6.5 and a hydroxyl number of from 50 to 600 mg KOH/g and polycarbonate polyols having a functionality of 2 and a hydroxyl number of from 50 to 600 mg KOH/g and combinations thereof, ii) at least one partially trimerized polyisocyanate having an isocyanurate content of from 15 to 95%, based on the sum of the number of isocyanate groups and isocyanurate groups, from the group consisting of diphenylmethane diisocyanate, the isomers thereof and higher homologues thereof (pMDI) and also mixtures thereof, toluylene diisocyanate and isomers and mixtures thereof, 1,6-hexamethylene diisocyanate, isophorone diisocyanate (IPDI), hydrogenated diphenylmethane diisocyanate (HMDI), the isomers and higher homologues thereof, pentane 1,5-diisocyanate and xylene 1,3-diisocyanate and also blends of the components of this group, iii) optionally polyfunctional amines, alcohols and hydroxyamines having molecular weights of less than 400 g/mol, in the presence of iv) optionally one or more urethaneization catalysts v) optionally one or more trimerization catalysts, where the NCO index (the ratio of the number of NCO groups to the number of OH groups multiplied by 100) when using polyols as component (i) is from 200 to 600 and the NCO index (the ratio of the number of NCO groups to the number of amine groups multiplied by 100) when using polyamines as component (i) is from 100 to 150. i) at least one isocyanate-reactive component from the group consisting of polyamines having a number average functionality of from ≥ 2 to ≤ 6.5 and a number average molecular weight of from 100 to 1000 g/mol, polyester polyols having a number average functionality of from ≥ 1.8 to ≤ 6.5 and a hydroxyl number of from 50 to 600 mg KOH/g, polyether ester polyols having a number average functionality of from ≥ 1.8 to ≤ 6.5 and a hydroxyl number of from 50 to 600 mg KOH/g and polycarbonate polyols having a functionality of 2 and a hydroxyl number of from 50 to 600 mg KOH/g and combinations thereof, ii) at least one partially trimerized polyisocyanate having an isocyanurate content of from 15 to 95%, based on the sum of the number of isocyanate groups and isocyanurate groups, from the group consisting of diphenylmethane diisocyanate, the isomers thereof and higher homologues thereof (pMDI) and also mixtures thereof, toluylene diisocyanate and isomers and mixtures thereof, 1,6-hexamethylene diisocyanate, isophorone diisocyanate (IPDI), hydrogenated diphenylmethane diisocyanate (HMDI), the isomers and higher homologues thereof, pentane 1,5-diisocyanate and xylene 1,3-diisocyanate and also blends of the components of this group, iii) optionally polyfunctional amines, alcohols and hydroxyamines having molecular weights of less than 400 g/mol, in the presence of iv) optionally one or more urethaneization catalysts v) optionally one or more trimerization catalysts, where the NCO index (the ratio of the number of NCO groups to the number of OH groups multiplied by 100) when using polyols as component (i) is from 200 to 600 and the NCO index (the ratio of the number of NCO groups to the number of amine groups multiplied by 100) when using polyamines as component (i) is from 100 to 150.