**Magnus Wenninger** was named Joseph Wenninger, taking the monastic name, Magnus after becoming a monk. His parents were both born in Germany and had emigrated to the United States, settling in Wisconsin. Magnus (we will refer to him by that name although at the time he was called Joe) was the second of his parents' seven children. His father was a baker in Park Falls, a town about 70 km south of the southern shore of Lake Superior. Magnus attended St Anthony Elementary School in Park Falls from 1925 to 1933. His parents expected the oldest of their boys to follow his father in becoming a baker, and Magnus as the second child to become a priest. When Magnus was about thirteen years old his parents saw an advertisement for Saint John's Preparatory School, Collegeville, Minnesota, in a German newspaper *Der Wanderer*. The monks and priests of Saint John's Abbey, a Benedictine community, had founded the school in 1857. The reason for the German connection was that the first Benedictines who came to Minnesota in 1856 came originally from the Bavarian abbey of Metten in southeastern Germany. The school prepared boys for the Benedictine college, St John's University, so Magnus's parents thought this would be the right place for Magnus to receive his education. He entered Saint John's Preparatory School in 1933 [1]:-

I was homesick being away at first, but by the end of the first year I had made so many friends and I liked it so much that I never left.

After graduating in 1937, Wenninger entered Saint John's University, Collegeville. He graduated with a B.A. in philosophy in 1942, having taken education as his minor subject. However, in parallel to this he had entered Saint John's Abbey and professed Benedictine monastic vows on 11 July 1940. He attended Saint John's Seminary and was ordained a Roman Catholic priest on 2 September 1945. When he entered the Order of Saint Benedict he was give the name Magnus so from this point on we will refer to him as Father Magnus. At this stage Father Magnus's education had not contained much mathematics. He explained in [1] how he was led to mathematics:-

After the usual high school courses, I had only one semester of college algebra in all my studies at St John's. One day, after I had been ordained a priest, the Abbot called me in to say that the Order was starting a school in the Bahamas, and he wanted me to go there and teach. "What will I teach?" I asked. "They'll tell you when you get there." But he said that before I went there, I should go to the University of Ottawa and get a Master's degree.

The Abbot suggested that he should study educational psychology. However [1]:-

When I got there I found that almost all of the courses I was interested in were being taught in French, which I had never learned. Fortunately there was one man there, Thomas Greenwood, in the philosophy department, who was willing to give me a course in English, in symbolic logic. I did my M.A. thesis on 'The Concept of Number According to Roger Bacon and Albertus Magnus'. It had to be done quickly, because I had to get ready to go down to the Bahamas.

After being awarded an M.A. in Philosophy from the University of Ottawa in 1946, Father Magnus was sent to St Augustine's College, Nassau, in the Bahamas. The headmaster of the school said he needed a teacher of English and a teacher of mathematics and gave Father Magnus the choice. Because of the mathematics he had studied during his Master's studies, he chose mathematics which, he said, proved to be the most significant decision in his life after deciding to become a Benedictine monk. His teaching was only at an elementary level but, after ten years, he felt rather stale and his headmaster suggested that he take a summer course. He decided to take a Master's Degree at Columbia University Teachers College in New York by studying there for four summer sessions. He was awarded his M.A. in Mathematics Education in 1961.

It was while studying at Columbia University Teachers College that he became interested in polyhedra after seeing models in display cases along the walls. He read *Mathematical Models* by H Martyn Cundy and A P Rollett, and then *The Fifty-nine Icosahedra* by H S M Coxeter, P Du Val, H T Flather and J F Petrie. After reading this book he began to make models of all the fifty-nine icosahedra and many of the uniform polyhedra. In 1966 the National Council of Teachers of Mathematics published Father Magnus's *Polyhedron Models for the Classroom. *The original booklet contained 40 pages but the revised edition, published in 1975, had 80 pages. Father Magnus writes in the Introduction:-

This booklet, first published in1966, went through its sixth printing in1973, making up a total of35000printed copies. That fact alone attests to the continuing interest in this work on the part of teachers and students alike.

His Abstract for this edition reads as follows:-

This second edition explains the historical background and techniques for constructing various types of polyhedra. Seven center-fold sheets are included, containing full-scale drawings from which nets or templates may be made to construct the models shown and described in the text. Details are provided for construction of the five Platonic solids, the thirteen Archimedean solids, stellations or compounds, and other miscellaneous polyhedra. The models may be used to illustrate the ideas of symmetry, reflection, rotation, and translation.

After the publication of the first edition of the booklet in 1966, Father Magnus had written to Donald Coxeter [1]:-

He was very helpful. He sent me a copy of the monograph on 'Uniform Polyhedra' written by himself, J C P Miller and M S Longuet-Higgins. That was the first time I saw a full list of the seventy-five uniform polyhedra. I started making the models one after the other, using cardstock paper, tagboard it was called. I made sixty-five of them, and they were on display in my classroom. At that point I decided to contact a publisher to see if they would be interested in a book. I sent the pictures and the text to Cambridge University Press.

Completing the task of constructing the remaining ten uniform polyhedra proved difficult and R Buckley of Oxford University assisted Father Magnus by supplying the precise measurements. Father Magnus published *Polyhedron models* with Cambridge University Press in 1971. Donald Coxeter wrote in the Foreword to the book:-

In his infectious enthusiastic style, the author gives clear instructions for making models of many kinds of polyhedra. These instructions are illustrated by photographs of his own collection, including what is almost certainly the only complete set ever made of the known uniform polyhedra. But photographs cannot really show the models in their full splendour. The most complicated 'snub' solids are not only extremely difficult to make but also highly decorative: a perfect instance of the connection between truth and beauty.

One might be surprised by Coxeter's phrase 'known uniform polyhedra', but he uses this with care since at the time of writing it was not known whether the 75 uniform polyhedra exhausted the list of such polyhedra. However, in 1975, John Skilling of Cambridge University proved, using a computer search, that the list was complete.

Arthur Loeb [6] writes in a review of *Polyhedron models*:-

The author describes with loving care the pitfalls or special effects to be encountered with each model, reflecting fifteen years of experience in the assembly of these fascinating and beautiful structures.

The book was also reviewed by D A Quadling [7] who writes:-

... and this is the book to give your favourite godchild, or perhaps your head of department on the occasion of his retirement(for there is material here for whiling away2000or more happy hours).

Father Magnus taught mathematics at St Augustine's College in Nassau until 1971, then spent the next ten years as Accountant and Comptroller for the College. In 1981 be returned to Minnesota and spent three years as Accountant in the Liturgical Press, Order of Saint Benedict, Collegeville. He then retired but continued to live at Saint John's Abbey, Collegeville.

Remarkably Father Magnus has published over 25 books and articles on mathematics, mostly on polyhedra. His articles include *Stellated Rhombic Dodecahedron Puzzle* (1963), *The World of Polyhedrons* (1965), *Some Facts About Uniform Polyhedrons* (1966), *Fancy Shapes from Geometric Figures* (1966), *Some Interesting Octahedral Compounds* (1968), *A New Look for the Old Platonic Solids* (1971), (with H Martyn Cundy) *A Compound of Five Dodecahedra* (1976), *Geodesic Domes by Euclidean Construction* (1978), *Avenues for Polyhedronal Research* (1980), *Polyhedrons and the Golden Number* (1990), and *Artistic Tessellation Patterns on the Spherical Surface* (1990).

To end this biography we look at two further books published by Father Magnus. The first of these is *Spherical models* (1979), which is described by E Jucovic in a review as follows:-

This is the author's second book on geometric models inspired by H S M Coxeter and is written in the same style as the first[Polyhedron models]. It describes precisely - with a minimum of theory - procedures for constructing(paper)models of special decompositions of the2-sphere(the regular and the Archimedean ones)and of geodesic domes and of some related models(honey-combs, etc.). By its contents the book should appeal mainly to students and teachers in mathematics, but it can be of interest to specialists in art, architecture and engineering. The book is illustrated by many excellent photographs and drawings, and effects nice aesthetic feelings.

The book was also reviewed by John Ede [4] who writes:-

This sequel to the author's 'Polyhedron Models' is all that devotees of the earlier book would expect; admirably clear, beautifully produced and alive with Magnus Wenninger's infectious enthusiasm. You may, like the reviewer, have made a great many models and may even be a byword for patience among your friends and yet you will surely feel faint at the thought of Wenninger's collection. This book is, however, more than instructions for a series of models: the underlying ideas are explained in enough detail to add greatly to one's satisfaction without taking control of what is intended as a practical book.

Also David Brisson [2] remarks that:-

... such a beautiful, clear and expository study of the class of forms presented by Wenninger is a delight.

The second of Father Magnus's two books we were going to look at is *Dual models* (1983). It was reviewed by Donald Coxeter:-

This book contains a beautifully illustrated description of the isohedral polyhedra whose vertices are surrounded like the apices of right pyramids based on regular polygons(including star polygons such as the pentagram). It begins with an enthusiastic foreword by Skilling, who once made an important contribution to the subject by establishing the completeness of the list of uniform polyhedra described by the author in his earlier book[Polyhedron models]. The introduction includes a careful description of the process of reciprocation with respect to a circle(in the plane)or a sphere(in space). This clarifies the principle(attributed to the late Dorman Luke)that the vertex figure of each uniform polyhedron yields by reciprocation the face of the dual polyhedron. Another useful principle, enunciated on page3, is that the dual of a given nonconvex uniform polyhedron π is a stellated form of the dual of the convex hull of π. Many pages are devoted to photographs of intricate models and well-illustrated instructions whereby the reader can try to duplicate this achievement. Two especially appealing solids, because of their extraordinarily sharp corners, are the great pentakisdodecahedron and the medial inverted pentagonal hexecontahedron.

Finally we quote from John Ede's review of the book [3]:-

Those model makers who already value 'Polyhedron Models' and 'Spherical Models' will welcome Wenninger's new book. Once again it is a volume that is a delight to handle, with clear diagrams and good photographs, and is a credit to publisher as well as author.

**Article by:** *J J O'Connor* and *E F Robertson*