In a community full of so-called "nerds", you are absolutely bound to get naming pedants. One of these people is me. This is a list of terms I dislike, their replacements and an explanation as to why I think they are wrong. It's worth noting that I don't usually use these if they deviate significantly from the standard naming scheme to the point of being difficult to understand. Also, the extent to which I wrote all of this may indicate some undiagnosed OCD. Incredible!
There are terms whose individual morphemes I consider incorrect for whatever reason. This category has a few (lot) of prescriptivistic pedantry. If you don't want to read about that, feel free to skip to Category II.
Cubohemioctahedron ->
A cuboctahedron faceting. Consistency reasons, only this shape uses the cubo- prefix.
Chasmic ->
Related to a feature in uniform polychora. Probably. Similar reason to prismatoid, shown below. Affects:
& chasmic cuboctachoron -> chasmatic cuboctachoron
& chasmic cupolic prismatooctachoron -> chasmatic cupolar prismatooctachoron
Cupol(a)ic ->
Relating to cupolae. More etymologically accurate and better sounding. A related fix is with its combining form:
& cupofastigium -> cupolifastigium
& pucofastigium -> pucolifastigium
There is also:
& rotundaeic (triangular hebesphenorotundaeic rhombochoron) -> rotundal
& pyramidic (small pyramidic swirlprism) -> pyramidal
Double antiprismoid ->
Family of polychora with swirl symmetry. The stem of Greek πρίσμα prísma is πρίσματ- prísmat-, yielding constructions such as disprismato. Prismoid would also fall into this rule, making the "more correct" spelling prismatoid. A related fix is with the prismatoid's dual, tegmoid being changed to tegmatoid.
Enneract ->
9-cube. Hypercubes are named by replacing the last vowel with an e of the Greek numeral representing the dimension. For 9, this results in enneë, the diaresis used to disambiguate from plain ee /iː/. Pronounced /ˈɛniːərækt/.
Fastegium ->
Lesser symmetrical version of a P-triangular duoprism. Correct Latin spelling.
Glomi- ->
Combining form of glome, the 3-sphere. Similar reason to prismatoid, shown below, although in this case the stem of Latin glomus is glomer-.
Gongol ->
4-ball. Correct Greek spelling, from γογγύλος gongýlos. Both spellings are commonly seen.
Nonagon ->
9-gon. In general, polygons use Greek prefixes: penta-, hexa-, hepta-, etc. The usual spelling of nonagon, however, breaks that pattern by using the Latin prefix nona- instead of the Greek ennea-. Already implemented in the polytopologist community.
Polychoric ->
Relating to polychora. In the case of polychora, polygons and polyhedra already use the -al adjectifier, with polychora and above breaking the pattern by using the -ic adjectifier, which to me also makes them uglier, especially in the case of -petic. This change also applies to higher ranks. Examples:
& pentachoric -> pentachoral
& isoteric -> isoteral
& heptapetic tetramyriatriacosicosaexic tegum -> heptapetal tetramyriatriacosicosaexal tegum
Quatro-icositetradiminished hexacosichoron ->
Convex polychoron, dual to the snub icositetrachoron. The first diminished polyhedra to be named only used the bi- and tri- prefixes, establishing a Latin numeral scheme. Continuations, however, use a Greek numeral scheme. The example on the title even uses a Portuguese-based system with quatro (4). One fix I've thought about is quattuor-quattuorAlthough if I were to care about impactfulness I wouldn't be writing this page. Examples:
& bi-icositetra
& tri-icositetra
& quattuor-icositetra
& tetracontocta
& heptacontadi
Tetracomb ->
Four dimensional (rank 5) tesselation. Somewhat useless hybrid word correction. Also applies to all >3D honeycombs. Similarly to the term it replaced while editing this page (seen in the HTML comment below tetracontoctachoron, 29 October 2025), this is quite volatile and subject to change.
& icositetrachoric tetracomb -> icositetrachoric fourcomb
& quarter penteractic pentacomb -> quarter penteractic fivecomb
& 222 hexacomb -> 222 sixcomb
& 521 octacomb -> 521 eightcomb
Tetracontoctachoron ->
The bitruncated 24-cell. This is more generally a "Greek numeral fix", also applying to most Greek prefixes for multiples of 10 as simply attaching -conta to a numeral is not (etymologically) correct. I also have made a generator for these prefixes at Numeral prefix generator.
& tetraconta -> tessaraconta (40)
& pentaconta -> penteconta (50)
& hexaconta -> hexeconta (60)
& heptaconta -> hebdomeconta (70)
& octaconta -> ogdoëconta (80)
& enneaconta -> eneneconta (90)
& enneacosi -> enacosi (900)
These are terms whose full name (composition of morphemes) I consider incorrect for whatever reason.
Disdyakis dodecahedron ->
Dual of the great rhombicuboctahedron. The name makes it seem like a disdyakis regular dodecahedron, which is not true. The shape is in fact a disdyakis rhombic dodecahedron, with disdyakis being the operation that adds augments rhombic faces, akin to triakis and tetrakis. Also applies to the disdyakis hexahedron (subsymmetrical version of the tetrakis cube) and the disdyakis triacontahedron, although the two are not as confusing.
Quasitruncated hexahedron ->
Quasitruncation of the cube and the conjugate of the truncated cube. No reason to spell it as hexahedron, especially when truncated cube is spelled as cube.
Rhombicuboctahedron ->
Expansion of the cube. Also applies to the other symmetries and quasis. Larger list of changes:
& rhombicuboctahedron -> small rhombicuboctahedron (sirco)
& quasi/great rhombicuboctahedron -> small quasirhombicuboctahedron (squerco)
& rhombicosidodecahedron -> small rhombicosidodecahedron (srid)
& quasi/great rhombicosidodecahedron -> small quasirhombicosidodecahedron (sqrid)
& rhombidodecadodecahedron -> small rhombidodecadodecahedron (sraded)
& quasidisprismatotesseractihexadecachoron -> small quasidisprismatotesseractihexadecachoron (squidpith)
Semistellated triacontaditeron ->
Dual of the demipenteract. Consistency with the demipenteract's demi- prefix. Semi- should imply a more general halfness instead of alternation.
Small rhombihexahedron ->
Faceting of the small rhombicuboctahedron. No reason to spell it as hexahedron, especially when there's also the small cubicuboctahedron.
Tetrakis hexahedron ->
Dual of the truncated octahedron. No reason to spell it as hexahedron.
Truncated cuboctahedron ->
Omnitruncation of the cube. Also applies to the other symmetries and quasis. Larger list of changes:
& truncated cuboctahedron -> great rhombicuboctahedron (girco)
& quasitruncated cuboctahedron -> great quasirhombicuboctahedron (gaquerco)
& truncated icosidodecahedron -> great rhombicosidodecahedron (grid)
& quasitruncated icosidodecahedron -> great quasirhombicosidodecahedron (gaqrid)
& truncated trihexagonal tiling -> great rhombitrihexagonal tiling (grothat)
& quasitruncated trihexagonal tiling -> great quasirhombitrihexagonal tiling (gaqrothat)
& (quasi)truncated dodecadodecahedron -> great rhombidodecadodecahedron (graded)
These are terms which are conceptually incorrect. Unlike the two categories above, I don't really understand their reasoning much as I'm mainly going by what people more knowledgeable than me say.
Cuboctatruncated cuboctahedron ->
A non-convex uniform polyhedron. Cuboctatruncation is not a thing that exists. Also applies to the other ABtruncated AB. Examples:
& cuboctatruncated cuboctahedron -> cubitruncated cuboctahedron (citco)
& icosidodecatruncated icosidodecahedron -> icositruncated dodecadodecahedron (itdid)
& tesseracti
& tesseracti
Faceted hexacosichoron ->
A starry regular polychoron. While not incorrect, there are eight other regular facetings of the hexacosichoron, along with billions if not trillions of nonregular nonconvex facetings. The adjective facetted, on the other hand, only allows that specific polychoron.
Great dirhombicosidodecahedron ->
An extremely complex uniform polyhedron. The name is simply just incorrect. There isn't even a small variant! Suggested by Pokemonkey (Discord message in Polytope Discord). The new name doesn't have the same flow though...
Hepteractidiminished laq ->
Laq (231 polyexon) diminished by the vertices of a 7-orthoplex. It is already standard that in names of the format [shape2]-diminished [shape1], the vertices of shape1 corresponding to the vertices of shape2 get removed, not the facets.
Pentagrammic double antiprismoid ->
Conjugate of the grand antiprism. It can be much more faithfully described as a retroprism than an antiprism, especially when it has pentagrammic retroprismatic cells. It could then also be called the grand retroprism. Pointed out by user Quasitruncated Hexahedron.
Pentagrammic rotunda ->
Conjugate of the pentagonal rotunda, half faceting of the great icosidodecahedron. Its segmentohedral representation makes use of retrograde pentagons (5/3). The "true" pentagrammic rotunda is another shape with pentagonal, pentagrammic and compound 10/2 faces. Also pointed out by user Quasitruncated Hexahedron.
Snub cube ->
An archimedean solid. The name snub cube implies, under the context of a facet-based scheme, that it has snub triangular faces and six square faces, which excludes the eight octahedral triangular faces. This applies to other "simple" snub polytopes. Examples:
& snub cube -> snub cuboctahedron (snico)
& snub dodecahedron -> snub icosidodecahedron (snid)
& snub pentachoron -> omnisnub pentachoron, snub decachoron (osnop/snad)
& snub tesseract -> omnisnub tesseract, snub tesseractihexadecachoron (osnet/sneth)
& snub icositetrachoron (not the uniform one) -> omnisnub icositetrachoron, snub tessaracontoctachoron (osni/snoc)
Tri-tridiminished icosahedron ->
Dual of the tridiminished icosahedron. The name tri-tridiminished implies it has 12−3×3 = 3 vertices, which is not true. Also, tristellated dodecahedron communicates its duality to the tridiminished icosahedron better.