# melle stoel

## Artists

## Statement

These artworks illustrate some of my discoveries of constructions which are possible to be made with antiprisms as explained in my papers. All odd p-antiprisms have got a uniform property; by attaching two antiprisms on an initial antiprism face-to-face on their equilateral triangular faces, the last, third antiprism is always placed 2/3 higher and also with its bases placed parallel with respect to the initial antiprism. From this theory several phenomena proceed which must be fascinating for lovers of such principles, just as Platonic and Archimedean solids can be constructed with 3-and-5-antiprisms. The 5-antiprism visualizes these phenomena in the artworks.

## Artworks

Of the alternating band of equilateral triangles which connects two parallel copies of a 5-gon three triangles are cut of across the top 5-gon. In the same way, from the bottom 5-gon another three triangles are cut of symmetrical with respect to the previous cut-of. Of solids which are now created a cycle is arranged such as the ones of the artwork ''Seoul''. Twelve cycles are attached as faces of a truncated icosahedron, not ''on'' each other but ''through'' each other, with an icosahedral angle. A cycle can be stacked on top of another which ables an arrangement of these solids to construct lattice walls in between the wig-shaped rest forms of these attached piles of cycle-faces of the truncated icosahedral sphere.

So as corkscrews can be formed, up and down moving cycles can be formed with any odd p-antiprism. These have a number of sides that depends on p, if p-antiprisms are used. For the matter of 5-antiprisms one obtains a 10-fold cycle. These bases of 5-antiprisms where all oriented in the same direction stil but since antiprisms are attached on their equilateral triangular faces, they can be turned in three different ways: left, right, or remain in the same position. For the matter of 5-antiprisms a turn to the left or right is one of an icosahedral angle; six 5-antiprisms fit inside an icosahedron. In this artwork these modificated cycles form a two- skinned rhombicosadodecahedral shere.

By using an odd p-antiprism, a corkscrew can be made whose cycle or cross-section has the shape of a d-gon, where d divides p. A corkscrew becomes a closed structure by stacking a pile of antiprisms on top of the first antiprism. The structure which is obtained with 5-antiprisms contains 7 pieces per side of the corkscrew which creates solid walls with diagonal buttress-like straight lines inside the wall's framework. These are also supported by extentions inside the corkscrew. Although their wouldn't be a match for, in a way the architectural construction reminds of the skeleton of a glass sponge.