Higher-dimensional geometry considers the properties of figures with four or more dimensions.
An object of zero dimensions is a single point. It needs no coordinates.
The first dimension takes up the space of a line, and has only one coordinate (the x coordinate).
The second dimension takes up the space of a plane, and has two coordinates, x and y. Examples of two-dimensional shapes are circles and squares.
The third dimension is all space that we know of, and it uses three coordinates, x, y, and z. Examples of three-dimensional shapes are cubes, spheres, and cones.
The fourth dimension is space with an extra dimension beyond the third, and it uses four coordinates, x, y, z, and w. Examples of four-dimensional shapes are the tesseract and the hypersphere.
Submit pages that deal with geometrical shapes or objects within a space of four or more dimensions. Sites about higher-dimensional polytopes in particular should be submitted to Science/Math/Geometry/Polytopes/Higher_Dimensional/.