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Artikel utama: Point groups in four dimensions
The  four-dimensional point groups (chiral as well as achiral) are listed in Conway and Smith, Section 4, Tables 4.1-4.3.
The following list gives the four-dimensional reflection groups (excluding those that leave a subspace fixed and that are therefore lower-dimensional reflection groups). Each group is specified as a Coxeter group, and like the polyhedral groups of 3D, it can be named by its related convex regular 4-polytope. Related pure rotational groups exist for each with half the order, and can be represented by the bracket Coxeter notation with a '+' exponent, for example [3,3,3]+ has three 3-fold gyration points and symmetry order 60. Front-back symmetric groups like [3,3,3] and [3,4,3] can be doubled, shown as double brackets in Coxeter's notation, for example [[3,3,3]] with its order doubled to 240.
| Coxeter group/notation | Coxeter group/notation | Coxeter diagram | Coxeter diagram | Order | Related polytopes |
| --- | --- | --- | --- | --- | --- |
| A4 | [3,3,3] |  |  | 120 | 5-cell |
| A4×2 | [[3,3,3]] |  |  | 240 | 5-cell dual compound |
| BC4 | [4,3,3] |  |  | 384 | 16-cell/Tesseract |
| D4 | [31,1,1] |  |  | 192 | Demitesseractic |
| D4×2 = BC4 | <[3,31,1]> = [4,3,3] |  | =  | 384 | Demitesseractic |
| D4×6 = F4 | [3[31,1,1]] = [3,4,3] |  | =  | 1152 | Demitesseractic |
| F4 | [3,4,3] |  |  | 1152 | 24-cell |
| F4×2 | [[3,4,3]] |  |  | 2304 | 24-cell dual compound |
| H4 | [5,3,3] |  |  | 14400 | 120-cell/600-cell |
| A3×A1 | [3,3,2] |  |  | 48 | Tetrahedral prism |
| A3×A1×2 | [[3,3],2] = [4,3,2] |  | =  | 96 | Octahedral prism |
| BC3×A1 | [4,3,2] |  |  | 96 | Octahedral prism |
| H3×A1 | [5,3,2] |  |  | 240 | Icosahedral prism |
| A2×A2 | [3,2,3] |  |  | 36 | Duoprism |
| A2×BC2 | [3,2,4] |  |  | 48 | Duoprism |
| A2×H2 | [3,2,5] |  |  | 60 | Duoprism |
| A2×G2 | [3,2,6] |  |  | 72 | Duoprism |
| BC2×BC2 | [4,2,4] |  |  | 64 | Duoprism |
| BC22×2 | [[4,2,4]] |  |  | 128 | Duoprism |
| BC2×H2 | [4,2,5] |  |  | 80 | Duoprism |
| BC2×G2 | [4,2,6] |  |  | 96 | Duoprism |
| H2×H2 | [5,2,5] |  |  | 100 | Duoprism |
| H2×G2 | [5,2,6] |  |  | 120 | Duoprism |
| G2×G2 | [6,2,6] |  |  | 144 | Duoprism |
| I2(p)×I2(q) | [p,2,q] |  |  | 4pq | Duoprism |
| I2(2p)×I2(q) | [[p],2,q] = [2p,2,q] |  | =  | 8pq | Duoprism |
| I2(2p)×I2(2q) | [[p]],2,[[q]] = [2p,2,2q] |  | =  | 16pq | Duoprism |
| I2(p)2×2 | [[p,2,p]] |  |  | 8p2 | Duoprism |
| I2(2p)2×2 | [[[p],2,[p]]] = [[2p,2,2p]] |  | =  | 32p2 | Duoprism |
| A2×A1×A1 | [3,2,2] |  |  | 24 | Duoprism |
| BC2×A1×A1 | [4,2,2] |  |  | 32 | Duoprism |
| H2×A1×A1 | [5,2,2] |  |  | 40 | Duoprism |
| G2×A1×A1 | [6,2,2] |  |  | 48 | Duoprism |
| I2(p)×A1×A1 | [p,2,2] |  |  | 8p | Duoprism |
| I2(2p)×A1×A1×2 | [[p],2,2] = [2p,2,2] |  | =  | 16p | Duoprism |
| I2(p)×A12×2 | [p,2,[2]] = [p,2,4] |  | =  | 16p | Duoprism |
| I2(2p)×A12×4 | [[p]],2,[[2]] = [2p,2,4] |  | =  | 32p | Duoprism |
| A1×A1×A1×A1 | [2,2,2] |  |  | 16 | 4-orthotope |
| A12×A1×A1×2 | [[2],2,2] = [4,2,2] |  | =  | 32 | 4-orthotope |
| A12×A12×4 | [[2]],2,[[2]] = [4,2,4] |  | =  | 64 | 4-orthotope |
| A13×A1×6 | [3[2,2],2] = [4,3,2] |  | =  | 96 | 4-orthotope |
| A14×24 | [3,3[2,2,2]] = [4,3,3] |  | =  | 384 | 4-orthotope |