Geometry (from the Ancient Greek: (γεωμετρία); geo - “earth”, -metron “measurement”) is a branch of Mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
In Mathematics and Physics, the dimensions of a space or object are informally defined in Euclidian Geometry as the minimum number of coordinates needed to specify any point within it.
Geometric Objects in higher Dimensions can be unfolded in lower Dimensions.
Although human beings only have immediate experience of the 3-Dimensional Space, this does not rule out at all the existence of other higher-numbered ones called Hyper-Spaces, the 4-Dimensional Space being one of them. They are therefore an infinity of higher dimensions.
Advanced physics such as String Theory considers higher dimensions. The Super-string Theory and M-Theory suggest that physical Space has ten and eleven dimensions, respectively. These extra dimensions are said to be spatial. However, we perceive only our 3-Dimension Space. A possible explanation that has been suggested is that Space acts as if it were “curled up” in the extra dimensions on a subatomic scale, possibly at the quark/string level of scale or below.
in Euclidean Geometry, HyperCubes are cubes in a Space of more than three dimensions. In a four dimensional Space the hypercube has a special name. It is called a Tesseract or 8-Cell. They consist of a cubic honeycomb that has 4 cubes around every edge, and 8 cubes around each vertex.
Graph of a Tesseract in the 3d Space
A 3D Projection of Tesseract
performing a double rotation