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In geometry of n dimensions or higher, a cantic n-cube, cantihalf n-cube, or truncated n-demicube is a uniform n-polytope, being a truncation of the n-demicube. It has half the vertices of a cantellated n-dimensional hypercube. It is a convex polytope.
Here are some examples:
| n | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|
| Symmetry [1+,4,3n-2] |
[1+,4,3] = [3,3] |
[1+,4,32] = [3,31,1] |
[1+,4,33] = [3,32,1] |
[1+,4,34] = [3,33,1] |
[1+,4,35] = [3,34,1] |
[1+,4,36] = [3,35,1] |
| Cantic figure |
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| Coxeter |      =   |
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| Schläfli | h2{4,3} | h2{4,32} | h2{4,33} | h2{4,34} | h2{4,35} | h2{4,36} |
