Non-spherical fine particles each having a polyhedral general shape with six or more surfaces each of which is formed as a concave surface, wherein the maximum external diameters L 1 of the non-spherical fine particles have an average value in the range of 0.1 - 20μm, wherein the ratios between the minimum external diameters L 2 and the maximum external diameters L 1 of the individual non-spherical fine particles have an average value in the range of 0.60 - 0.97, wherein said non-spherical fine particles have an average number per particle of 6 - 14 concave surfaces of which the ratio of the maximum diameter m 1 with respect to the maximum external diameter L 1 is in the range of 0.20 - 0.90, and wherein the average values are values obtained from arbitrarily selected 20 of a scanning electron microscope photograph image of said non-spherical fine particles and the number of concave surfaces per non-spherical fine particle is defined as being twice the number of concave surfaces observed on said scanning electron microscope photograph image wherein the non-spherical fine particles comprise siloxane units SiO 2 in an amount of 30 - 50 molar %, siloxane units R 1 SiO 1.5 in an amount of 40 - 60 molar % and siloxane units R 2 R 3 SiO in an amount of 5 - 20 molar % so as to be a total of 100 molar %, wherein R 1, R 2 and R 3 are each alkyl group with 1 - 4 carbon atoms or phenyl group and the particles are prepared by a method comprising the steps of: using silanol group forming silicide SiX 4 in an amount of 30 - 50 molar %, silanol group forming silicide R 4 SiY 3 in an amount of 40 - 60 molar % and silanol group forming silicide R 5 R 5 SiZ 2 in an amount of 5 - 20 molar % so as to be a total of 100 molar %; generating a silanol compound by causing silanol group forming silicide SiX 4 to contact water in the presence of an acidic catalyst so as to undergo hydrolysis; and causing a condensation reaction of said silanol compound with silanol group forming silicide R 4 SiY 3 and silanol group forming silicide R 5 R 6 SiZ 2 in an aqueous condition in the presence of an acidic catalyst and a nonionic surfactant; wherein R 4, R 5 and R 6 are each alkyl group with 1 - 4 carbon atoms or phenyl group, and X, Y and Z are each alkoxy group with 1-4 carbon atoms, alkoxyethoxy group having alkoxy group with 1-4 carbon atoms, acyloxy group with 2-4 carbon atoms, N,N-dialkylamino group having alkyl group with 1-4 carbon atoms, hydroxyl group, halogen atom or hydrogen atom. using silanol group forming silicide SiX 4 in an amount of 30 - 50 molar %, silanol group forming silicide R 4 SiY 3 in an amount of 40 - 60 molar % and silanol group forming silicide R 5 R 5 SiZ 2 in an amount of 5 - 20 molar % so as to be a total of 100 molar %; generating a silanol compound by causing silanol group forming silicide SiX 4 to contact water in the presence of an acidic catalyst so as to undergo hydrolysis; and causing a condensation reaction of said silanol compound with silanol group forming silicide R 4 SiY 3 and silanol group forming silicide R 5 R 6 SiZ 2 in an aqueous condition in the presence of an acidic catalyst and a nonionic surfactant; wherein R 4, R 5 and R 6 are each alkyl group with 1 - 4 carbon atoms or phenyl group, and X, Y and Z are each alkoxy group with 1-4 carbon atoms, alkoxyethoxy group having alkoxy group with 1-4 carbon atoms, acyloxy group with 2-4 carbon atoms, N,N-dialkylamino group having alkyl group with 1-4 carbon atoms, hydroxyl group, halogen atom or hydrogen atom.