Escher also worked on regular solids, known as polyhedra, that he extensively explored in many of his works. His woodcut “Three Intersecting Planes” is an especially illuminating example of this. In the present exhibit, the simple fact that two planes meet along an edge and that three planes meet at a vertex is demonstrated in an aesthetically appealing way.

This exhibit is an extension of the tensegrity structure concept that brings out a further advantage or effectiveness, namely robustness and structural stability. For the struc- ture to weather a storm or a tremor, it needs to absorb sudden shocks and regain the original form

Where do these occur? Spider web example again relates this aspect to the fact that the web isn’t easily destroyed by strong winds or by violent disturbances caused at the anchored ends. Being one of the most commonly found designs in nature, the radial threads connected to fixed objects are crisscrossed by the spiral threads to form an optimal design. It is strong enough to hold a large prey and at the same time flexible enough to sustain strong wind blows. Recent studies show that if few local threads are broken, the overall loading capacity of the web is in fact increased, proving the robustness of the structure. When a prey is trapped, the spider gets the message through the vibrations of threads. The patterns of interwoven threads enables the spider to spot the prey in an efficient manner.

‘Tensegrity' is an amalgamation of two words `Tension' and `Integrity.' Tensegrity concept is mainly about the judicious use of available material to create a structure that is both stable and spans a large area; it is used to build structures which employ an economy of material and obtain optimal results. Tensegrity structures contain two types of components to achieve this purpose: the struts which lend strong support, that is the integrity part, and the cables that maximize the span by stretching or tension. In other words, strong struts connected together by flexible cables hold the structure together in optimal tension.

Where do such structures occur? In nature, spider webs demonstrate this concept effectively: they contain strong structural supports, the radial threads and a few polygonal threads, and the rest of the web is woven around it. Mathematically, tensegrity is a configuration of points, or vertices, that satisfy some simple distance constraints. Cables keep vertices close together and struts hold them apart. Another main purpose in building structures employing this concept is also to achieve quick assembling and dissembling so as to enable ease of transportation.

The tensegrity stool is one example of this structural concept. It basically consists of rods and strings connected together to support either a human or an object placed on it.

Symmetry abounds in nature. In every glance our eyes notice, almost seek out, symmetry. Nature shows us symmetry in abundance. Whether we look at the shell of a tortoise, a honeycomb (beehive) or even plant tissue through a microscope we find a discernible pattern. A pattern that is repeated over and over. It is this symmetry that is reflected in almost all designs made by humans as well. A tessellation is a way of covering a (flat) surface with tiles in such a manner that there are no gaps or overlaps. The idea behind building a tessellation is simple; take a pattern or tile and repeat it over the entire surface. Just like a plasterer mason tiles a floor! There are many different types of tessellations – different shapes can be used to tile a surface. The most commonly seen tiles are polygons.

Regular Tessellations. A regular tessellation is a pattern which uses polygons to tile a planar surface. A polygon with n sides is called an n-gon. For instance, a triangle is a 3-gon; a square, rectangle or a quadrilateral is a 4-gon; a pentagon is a 5-gon; and so on. Strictly speaking a regular tessellation uses exactly one type of tile, like the patterns usually seen on the floor, or in a honeycomb. The simplest way to tile a surface is to use a regular n-gon as a tile. A regular n-gon is an n-gon where all sides have equal length, like an equilateral triangle or a square. Ever wonder why we don’t see pentagons used to tile a surface? As illustrated by the exhibit, when one uses equilateral triangles, squares or regular hexagons then it is possible to construct a tessellation. But it doesn’t work with regular pentagons.