European Journal of CombinatoricsVolume 3, Issue 3, September 1982, Pages 255-258On Spherical t-designs in ℝ2Author links open overlay panelYiming HongShow moreShareCitehttps://doi.org/10.1016/S0195-6698(82)80036-XGet rights and contentUnder an Elsevier user licenseopen archiveLet X be a spherical t-design in ℝ2 with |X| = n. It is shown that: (i)for t + 1 ⩽ n ⩽ 2t + 1, X must be a regular n-gon(ii)for n = 2t + 2, X is the union of two regular (t+1)-gons(iii)for each n⩾2t+3, there are many (ℵ1) X's which can not be decomposed into the union of regular ki-gons where ki ⩾ (t + 1).Previous article in issueNext article in issueRecommended articlesCited by (0)Copyright © 1982 Academic Press Inc. (London) Limited. Published by Elsevier Ltd. All rights reserved.