Tesseract
How to see a cube in four dimensions.
01 Shadow
A shadow is one dimension less.
3D cube→2D shadow
θ
02 Shadow, one step up
A 4D cube casts a 3D shadow.
4D tesseract→3D shadow
xw
03 Slice
Cut a cube, get a polygon.
2D
3D cube∩plane→2D polygon
z
04 Slice, one step up
Cut a tesseract, get a solid.
+w−w
4D tesseract∩3D space→3D solid
w
05 Build it
Now build one yourself.
2Dsegment → square
3Dsquare → cube
4Dcube → tesseract