Visualization of a Die and Other Objects in Four-Dimensional Space

This paper proposes a geometric method for imagining and constructing the 4-dimensional analogue of a 3-dimensional object, in this case a cubical die. First, a 4-dimensional analogue of a rolling 3-dimensional die is imagined in 4-space according to geometric properties. Second, it is projected orthogonally into 3-space as a solid that is shown by orthogonal projection onto a plane. Lastly, this procedure is applied to other images to illustrate additional 4-dimensional analogues of 3-dimensional objects.