Nets of 5-cells and 8-cells Regular Polytopes.
Above is a picture of a net of 5-cells polytope. This polytope is a 4-dimensional regular pyramid. Each cell of this polytope is a regular tetrahedron (see Plato’s polyhedrons). A construction of such net is not unique. This time a net is a regular tetrahedron W and 4 the same regular tetrahedrons glued to each face of W. These 4 tetrahedrons hide tetrahedron W, hence W cannot be seen.
There is an easy explanation how to receive a regular 5-cells polytope from this net. Consider 4 outer tetrahedrons of this net. In 4-dimensional space they can be rotated about the face common with W. Let us rotate them the way that all outer vertices coincide and we’ll receive required polytope.
Let us present another net of this polytope:
Let us turn to 8-cells regular polytope. It is also called hypercube. Let us present 2 pictures of a net of this polytope:
As before this net is not unique. Let us show another way of construction:
See new applets of ‘Literka’:
Applet: Cross sections of a regular 8-cells and 24-cells polytope.
Applet: Cross sections of a regular 600-cells polytope.
See pages of ‘Literka’ about cross sections of other regular polytopes:
Hypercube,
16-cells Polytope,
24-cells Polytope,
120-cells Polytope,
600-cells Polytope.
See pages about nets of:
16-cells and 24-cells polytope.
See pages about polytopes built of congruent bipyramids:
Four examples of polytopes built of congruent bipyramids.
Two examples of polytopes built of congruent bipyramids.
Applet: Cross sections of 2 polytopes built of congruent bipyramids (24 and 32 cells).
Applet: Cross sections of 2 polytopes built of congruent bipyramids (720 and 1200 cells).
Applet: Cross sections of polytopes built of congruent bipyramids (96 cells).
Return to the list of pages of 'Literka' about polytopes.
Return to the main geometrical page of 'Literka'.
Return to the main page of 'Literka'.