Higher Dimensional Polytope Nets
The geometric concept of a net can be extended to higher dimensions.
Tesseract |
Truncated tesseract |
24-cell |
For example, a net of a polychoron, or four-dimensional polytope, is composed of polyhedral cells that are connected by their faces and all occupy the same three-dimensional space, just as the polygon faces of a net of a polyhedron are connected by their edges and all occupy the same plane. The above net of the tesseract, the four-dimensional hypercube, is used prominently in a painting by Salvador Dalí, Crucifixion (Corpus Hypercubus) (1954).
Whether or not every four-dimensional polytope may be cut along the two-dimensional faces shared by its three-dimensional facets, and unfolded into 3D to a single nonoverlapping polyhedron (as in the above unfolding of the tesseract), remains unknown, as does the corresponding question in higher dimensions.
Read more about this topic: Net (polyhedron)
Famous quotes containing the words higher, dimensional and/or nets:
“The true thrift is always to spend on the higher plane; to invest and invest, with keener avarice, that he may spend in spiritual creation, and not in augmenting animal existence. Nor is the man enriched, in repeating the old experiments of animal sensation; nor unless through new powers and ascending pleasures he knows himself by the actual experience of higher good to be already on the way to the highest.”
—Ralph Waldo Emerson (1803–1882)
“I don’t see black people as victims even though we are exploited. Victims are flat, one- dimensional characters, someone rolled over by a steamroller so you have a cardboard person. We are far more resilient and more rounded than that. I will go on showing there’s more to us than our being victimized. Victims are dead.”
—Kristin Hunter (b. 1931)
“Translation is entirely mysterious. Increasingly I have felt that the art of writing is itself translating, or more like translating than it is like anything else. What is the other text, the original? I have no answer. I suppose it is the source, the deep sea where ideas swim, and one catches them in nets of words and swings them shining into the boat ... where in this metaphor they die and get canned and eaten in sandwiches.”
—Ursula K. Le Guin (b. 1929)