HEXA/The divisions of Hexacube/CUBE

HEXA CUBE

　

Hexacube is a mathematical model to measure 3-D depth.

Six diagonal lines of hexacube make a hexagram. These diagonal are the axes to measure length,widh and hight of solid objects. Then the accurate picture or the solid object could be made by drawing lines from the three radial lines to the measured points, on the axes.

Two regular triangles which stand opposite are the standard lines to measure inside-outside a solid.

A cube is made up by drawing lines between eight vertexes of
two regular tetrahedra.
Edges of the regular tetrahedra are diagonal lines of the cube.

metamorphose of hexa cube

Hexacube, where a hexagram that consists of edges of two regular tetrahedral exists it's inside, is a mathematical model to represent a 3-D basic structure of hexagram geometry.

It could be a basic unit to measure the space where both parts and the whole are changing, keeping their structure in the frame of radiating lines.

Serially changing each Hexacube always keeps
the same relationship to the whole.　

立方体

The divisions of Hexacubes which has self-similarity.

cube
HEXACUBE

By unfolding a cube and two regular tetrahedra, it becomes clear that edges of tetrahedral are diagonals of six squares and one is right angle with another.

Hexa polyhedron dice	Hexa polyhedron consists of two regular tetrahedron. It's eight vertexes are also vertexes of a cube. Lines between vertexes form twelve edge of the cube. Hexa polyhedron seems to be inside the cube but in reality it's surfaces are same level with the cube's because the edge of the regular tetrahedron are the diagonals of the cube's surfaces at the same time.