If you are fascinated by higher dimensions, here is something to get your teeth into… These are orthographic (2D or flat) projections of analogues of the cube from dimensions zero-ten. The higher dimensional analogues can also be called hypercubes, or n-cubes where “n” is the number of dimensions. The term “n-cube” is also used for the lower dimensional projections. so a line is called a 1-cube and a square is a 2-cube and so on.. A tesseract is constructed by connecting the vertices of two cubes through a fourth dimension. The penteract is constructed by connecting the vertices of two tesseracts through a fifth dimension. Have a look at how the cube is oriented and try to visualise how the hypercubes are constructed.. it is not as hard as it looks..
Le “Pater Noster, The Lord’s Prayer James Tissot (1836–1902)
Our Father who art in heaven, hallowed be thy name. Thy kingdom come. Thy will be done on earth as it is in heaven. Give us this day our daily bread, and forgive us our trespasses, as we forgive those who trespass against us, and lead us not into temptation, but deliver us from evil.
This is a tesseract. A tesseract is the four dimensional analogue of the cube.
The cube is to the tesseract what the square is to the cube. The cube has a surface composed of six faces (squares). A tesseract has a hypersurface composed of eight cells (cubes) and is also called an octachoron or 8-cell. You can also call a tesseract a hypercube. The prefix hyper- simply means it has more thanthree dimensions. You can also have 5D hypercube. Of course we cannot physically construct a tesseract in four dimensions, but we can create a projection in two or three dimensions,
The easiest way to draw a tesseract is to connect the vertices of two cubes. Compare it to the drawing of a cube, where you connect the vertices of two squares. Remember that you are only looking at a lower dimensional “shadow” of a tesseract. All cubes in the tesseract are the same size. The cube in the centre appears smaller because it is further away in four dimensions.