The polytopal association scheme (Q1058249)

In the first author and \textit{D. C. Frank}, Can. J. Stat. 2, 45-59 (1974; Zbl 0374.62071), a family of m-associate class partially balanced association schemes (PBAS(m)) was defined by considering n treatments as being clustered at each of the s vertices of a regular s-sided polygon. This polygonal association scheme and the resulting partially balanced incomplete block designs were studied in detail for \(s=3,4,5\) and 6. In the present paper, the ideas begun in the quoted paper are extended to general s-sided polygons (Section 4), to p-dimensional polytopes (Section 3), and to five regular polyhedra in three dimensional space (Section 5).