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A Topological Puzzle


When 40 of the Anolatabulata forms were exhibited at the New Gallery, it was possible visually to sort these shapes into several different “families”. Nevertheless I could not discern the relationship of these families one to another nor the underlying structure. In attempting to understand this complexity I studied the shapes via a series of free-hand charcoal drawings – see (i),(ii).


Then, some time after the New Gallery exhibit, I sought the advice of Professor Philip Huneke of Ohio State University’s Department of Mathematics. Phil was particularly interested in the 12 congruent shapes made by combining 4 identical dewdrop shapes. He determined schematically that these could be placed on a triangular shape so that each form transformed into the next. See (iii). This triangle was marked, folded, seamed and inflated to form a Zeeman’s Dunce Cap. This was of such interest to him that he presented a paper at the Summer Session of the American Mathematical Society entitled “Smooth Tessellations of a Sphere (`a la Betty Collings) and other surfaces. A summary of this presentation was published in the exhibition catalogue for “Drawing on Sculpture” presented at the Bertha Urdang Gallery, N.Y., in 1979. (See Selected Curatorial Essays).


Not entirely with Phil’s approval the Dunce Cap idea was developed by making a large field from two triangles on which all the form names were printed with ink colored according to the sub-category or shape, (iv). The two principal triangles from this 9’6’ x 54’ vinyl sheet were cut out, next two Zeemans were folded then seamed together and inflated so that “Double Zeeman” became a plan for the three dimensional placement of all the forms, (v); (vi – vii).

(ii) Line Study "Anolatabulata 3g"
drawing. c 1975 Charcoal on
Newsprint. 18"x25"
(i) Line Study "Anolatabulata 12h"
c.1975 Charcoal on newsprint.



(iii) Schematic for placement
on Zeeman's Dunce Cap.
(iv) Schematic for "Double Zeeman"



(v) "Double Zeeman" Print. 1978-9. Acrylic on vinyl. 54"x114"



(vi) (vii) Two views of completed "Double Zeeman" 1978-79. Approx. 36"x36"
Photo: W. Weider
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