## K-science

An eleven sided spatial form with unique optical, acoustical and structural properties. Discovered by Janusz Kapusta in 1985, and patented in 1987.

Two K-drons with a 45 degree angle of inclination placed on top of each other form a cube.

Stretched K-drons form new proportions but preserve their properties.

Two opposite forces applied on a flat rubber plane create K-dron’s surface. The angle of inclination is proportional to the amount of applied force.

To a string placed in space-time coordinate system, a force (represented by red arrow) is applied. When the force is released the vibrating string on its way from top to bottom in its mathematical model reveals the surface of K-dron. The fact that the K-dron surface can be related to both the symmetry of a cube and the solution to the wave equation is deeply significant.

It is its unique property that 2 K-drons can form a cube and 8 such elements can enclose a sphere like shape or more precisely a rhombic dodecahedron.

The animation shows simple reconstruction of K-dron, whichis built from three squares and one rectangle. The arrow indicates that the longer side of the rectangle is equal to the diagonal of the square. These three squares and the rectangle divided into 11 pieces form K-dron’s shape.

A cube sliced by planes along all axes of its symmetry will create 48 pyramids. There is no K-dron in such a divided cube but 4 cubes put it on top of each other easily reveal K-dron. This part of K-dron presentation is specially important because it discovers its own location in dense matter of space. In the world filled infinitely with cubes and divided by planes along all axes, K-dron’s net has always existed. In another words, K-dron could be considered as a new important dynamic net moved a half module to the side and down (or up) in relation to the static net of cubes.

One black and one white K-dron combined together form a cube. 4 such cubes (4 white and 4 black K-drons) can generate one of 38,416 surface pattern combinations.

Janusz Kapusta’s first visualization of K-dron surface appearing as two perspectives progressing towards two opposite and infinite directions.

Taking one quarter of each octahedron, black representing exterior, white interior, can create a surface of K-dron.

A group of K-drons can be placed on a square grid in many different arrangements. Any arrangement interacts dramatically with light and shadow. When the angle of light changes, entire new groups of visual patterns are created.

Animations by Janusz Kapusta and Przemyslaw Moskal.