Hexic 7-cubes
Open-knowledge reference entry
In seven-dimensional geometry, a hexic 7-cube is a convex uniform 7-polytope, constructed from the uniform 7-demicube. There are 16 unique forms.
Hexic 7-cube
Alternate names
Small terated demihepteract (acronym: suthesa)
Cartesian coordinates
The Cartesian coordinates for the vertices of a hexic 7-cube centered at the origin are coordinate permutations:
(±1,±1,±1,±1,±1,±1,±3)
with an odd number of plus signs.
Images
Hexicantic 7-cube
Alternate names
Teritruncated demihepteract (acronym: tuthesa)
Images
Hexiruncic 7-cube
Alternate names
Terirhombated demihepteract (acronym: turhesa)
Images
Hexisteric 7-cube
Alternate names
Teriprismated demihepteract (acronym: tuphesa)
Images
Hexipentic 7-cube
Alternate names
Tericellated demihepteract (acronym: tuchesa)
Images
Hexiruncicantic 7-cube
Alternate names
Terigreatorhombated demihepteract (acronym: tugrohesa)
Images
Hexistericantic 7-cube
Alternate names
Teriprismatotruncated demihepteract (acronym: tupthesa)
Images
Hexipenticantic 7-cube
Alternate names
Tericellitruncated demihepteract (acronym: tucothesa)
Images
Hexisteriruncic 7-cube
Alternate names
Teriprismatorhombated demihepteract (acronym: tuprohesa)
Images
Hexipentiruncic 7-cube
Alternate names
Tericellirhombated demihepteract (acronym: tucrohesa)
Images
Hexipentisteric 7-cube
Alternate names
Tericelliprismated demihepteract (acronym: tucophesa)
Images
Hexisteriruncicantic 7-cube
Alternate names
Terigreatoprismated demihepteract (acronym: tugphesa)
Images
Hexipentiruncicantic 7-cube
Alternate names
Tericelligreatorhombated demihepteract (acronym: tucagrohesa)
Images
Hexipentisteriruncic 7-cube
Alternate names
Tericelliprismatorhombated demihepteract (acronym: tucprohesa)
Images
Hexipentistericantic 7-cube
Alternate names
Tericelliprismatotruncated demihepteract (acronym: tucpathesa)
Images
Hexipentisteriruncicantic 7-cube
Alternate names
Great terated demihepteract (acronym: guthesa)
Images
Related polytopes
These polytopes are based on the 7-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC7 symmetry, and 32 are unique:
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973
Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com, ISBN 978-0-471-01003-6
(Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559–591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit.
This brief starts where responsible research should: with the source description of “Hexic 7-cubes” as open-knowledge reference entry. Everything that follows is an evidence route, not borrowed authority.
Why this record matters
The subject matters to the general reference register because the source frames it as open-knowledge reference entry. Its deeper value depends on whether names, dates, institutions and citations support that framing.
The citation trail is more important than the brevity of the summary: it shows where individual claims can be examined in context. The source revision retrieved here is dated Apr 17, 2026. The linked authority identifier is Q17099558. The first chronological checks are 1973, 1995, 1940 and 1985.
Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Hexic 7-cubes”, its source revision and the description used here.
- Expand the search: follow Hexic 7-cubes primary sources, Hexic 7-cubes archive and Hexic research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Hexic 7-cubes”?
- What terminology or title could unlock a more precise catalogue search?
- Which cited source is closest to the event, object or claim?
Search terms from this dossier
This entry incorporates text from “Hexic 7-cubes” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.