Higher Dimensions
This alternation operation applies to higher dimensional polytopes and honeycombs as well, however in general most forms won't have uniform solution. The voids created by the deleted vertices will not in general create uniform facets.
Examples:
- Honeycombs
- An alternated cubic honeycomb is the tetrahedral-octahedral honeycomb.
- An alternated hexagonal prismatic honeycomb is the gyrated alternated cubic honeycomb.
- Polychora
- An alternated truncated 24-cell is the snub 24-cell.
- A hypercube can always be alternated into a uniform demihypercube.
- Cube → Tetrahedron (regular)
- →
- Tesseract (8-cell) → 16-cell (regular)
- →
- Penteract → demipenteract (semiregular)
- Hexeract → demihexeract (uniform)
- ...
- Cube → Tetrahedron (regular)
Read more about this topic: Alternation (geometry)
Famous quotes containing the words higher and/or dimensions:
“Universal empire is the prerogative of a writer. His concerns are with all mankind, and though he cannot command their obedience, he can assign them their duty. The Republic of Letters is more ancient than monarchy, and of far higher character in the world than the vassal court of Britain.”
—Thomas Paine (1737–1809)
“Why is it that many contemporary male thinkers, especially men of color, repudiate the imperialist legacy of Columbus but affirm dimensions of that legacy by their refusal to repudiate patriarchy?”
—bell hooks (b. c. 1955)