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)
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