Shape
Faces: 24
Cells: 8
Edges: 32 Vertex figure: Tetrahedron Vertices: 16
Properties: convex, isogonal isotoxal, isohedral
Petrie polygon: octagon
Tesseract is a cube in 4-dimensional space. You could also say that it's the 4D analogue of a cube. It is a 4D shape where every face is a cube.
Construction
The construction of hypercubes can be imagined the following way:
1-dimensional: Two points A and B can be connected to become a line, giving a new line segment AB.
2-dimensional: Two parallel line segments AB and CD can be connected to become a square, with the corners marked as ABCD.
3-dimensional: Two parallel squares ABCD and EFGH can be connected to become a cube, with the corners marked as ABCDEFGH.
4-dimensional: Two parallel cubes ABCDEFGH and IJKLMNOP can be connected to become a tesseract, with the corners marked as ABCDEFGHIJKLMNOP.
Volume
V = L⁴
The tesseract has volume L•L•L•L. It is bounded by faces on 8 sides. The faces are cubes of volume L³. We know there are 8 of them since its four dimensional axes must be capped on either end by faces--two cubical faces per axis. Once again, we cannot visualize all four of these capped dimenions. We can at best visualize three directions perpendicular to each other.
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