The process of producing the facial planes of a polyhedron to form stellated polyhedra is well known. When applied to the icosahedron it leads to a series which is limited to eight solids if we make the condition that every face of each must be covered in forming the next of the series. If this condition is dropped a large number of combinations of the parts of these eight solids is possible. The total number of solids, limited by symmetry considerations, is 59, and they are all illustrated in The 59 Icosahedra by Coxeter, Du Val, Flather, and Petrie. The corresponding basic series of solids starting with the Rhombic Triacontahedron numbers 13, and the total number of combinations is very great.

After constructing Platonic solids, Archimedean solids and some of the Kepler-Poinsot polyhedra, I became interested in zonohedra, like the rhombic dodecahedron and triacontahedron shown in Fig. 1. These

models were new to me and most of what I knew about them at that time is summed up by H. S. M. Coxeter in his book Regular polytopes as follows:

The following treatment is perhaps easier than, and is in son respects an expansion of, that given by Professor H. F. Baker in h Principles of Geometry, vol. ii, pp. 58-60.

1. A,B,C,O are four given points ; AO meets BG in D, BO meet CA in E, CO meets AB in F. Then DEF is the diagonal point triangle of the quadrangle ABCO. Take this as triangle of reference for areal coordinates and let O be (u, v, w). Then A is (-u, v, w) B is (u, - v, w) and C is (u, v, -w).

The most important properties of any distribution are its moments. The first four moments, for example, can be used describe any data set fairly well. Moments can also be used for estimation.

The earlier sections of this account are concerned with some standard properties of pure recurring decimals. These include the cyclic property, illustrated for example by the decimals representing the six proper fractions with denominator 7, each of which has a period using a cyclic permutation of the digits 142857 It was a question concerning this property, raised by a student, which led to the writer's interest in the properties considered in the later sections. References are given in Dickson's History of the Theory of Numbers, Vol. I, Ch. 6.

A recent conference, held at Southampton early in September, marked the end of the first stage, and of the first twelve months’ work, of this Project. Its objectives are now well-known, namely, the experimental introduction of entirely new mathematical syllabuses in certain schools, together with the setting of appropriate G.C.E. papers, and the writing of text-books and teachers’ guides. But it may be of some interest to fill in some further details of the work.