Steric 5-cubes

In five-dimensional geometry, a steric 5-cube, steric 5-demicube or sterihalf 5-cube, is a convex uniform 5-polytope. There are unique 4 steric forms of the 5-cube. Steric 5-cubes have half the vertices of stericated 5-cubes.

Steric 5-cube

Alternate names

• Steric penteract, runcinated demipenteract
• Small prismated hemipenteract (siphin) (Jonathan Bowers)

Cartesian coordinates

The Cartesian coordinates for the 80 vertices of a steric 5-cube centered at the origin are the permutations of

(±1,±1,±1,±1,±3)

with an odd number of plus signs.

Images

Related polytopes

Stericantic 5-cube

Alternate names

• Prismatotruncated hemipenteract (pithin) (Jonathan Bowers)

Cartesian coordinates

The Cartesian coordinates for the 480 vertices of a stericantic 5-cube centered at the origin are coordinate permutations:

(±1,±1,±3,±3,±5)

with an odd number of plus signs.

Images

Steriruncic 5-cube

Alternate names

• Prismatorhombated hemipenteract (pirhin) (Jonathan Bowers)

Cartesian coordinates

The Cartesian coordinates for the 320 vertices of a steriruncic 5-cube centered at the origin are coordinate permutations:

(±1,±1,±1,±3,±5)

with an odd number of plus signs.

Images

Steriruncicantic 5-cube

Alternate names

• Great prismated hemipenteract (giphin) (Jonathan Bowers)

Cartesian coordinates

The Cartesian coordinates for the 960 vertices of a steriruncicantic 5-cube centered at the origin are coordinate permutations:

(±1,±1,±3,±5,±7)

with an odd number of plus signs.

Images

Related polytopes

These polytopes are based on the 5-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.

There are 23 uniform polytera (uniform 5-polytopes) that can be constructed from the D5 symmetry of the 5-demicube, 8 of which are unique to this family, and 15 are shared within the 5-cube family.

Further reading

• Coxeter, H. S. M. (1973). (3rd ed.). New York City: Dover.

• Coxeter, H. S. M. (1995-05-17). Sherk, F. Arthur; McMullen, Peter; Thompson, Anthony C.; Weiss, Asia Ivić (eds.). . Canadian Mathematical Society Series of Monographs and Advanced Texts. John Wiley & Sons. ISBN 978-0-471-01003-6. LCCN . OCLC . OL .

• Coxeter, H. S. M. (1940-12-01). . Mathematische Zeitschrift. 46. Springer Nature: 380–407. doi:. ISSN . S2CID .

• Coxeter, H. S. M. (1985-12-01). . Mathematische Zeitschrift. 188 (4). Springer Nature: 559–591. doi:. ISSN . S2CID .

• Coxeter, H. S. M. (1988-03-01). . Mathematische Zeitschrift. 200 (1). Springer Nature: 3–45. doi:. ISSN . S2CID .

• Johnson, Norman W. (1991). Uniform Polytopes (Unfinished manuscript thesis).

• Johnson, Norman W. (1966). (PhD thesis). University of Toronto.

External links

• Weisstein, Eric W. . MathWorld.