S&T Nom Diagramme Degrés Codegrés

Orbites d’hyperplans Corps

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A_{r}  ◯_{s_{1}} ◯_{s_{2}}⋯◯_{s_{r}}  2, 3, …, r + 1  0, 1, …, r − 1  s_{1}: \frac{r(r+1)}{2}  ℚ  1  (s_{1} … s_{r})^{r+1}

G_{4}  A_{2}^{(3)}  ◯_{s}_{3}  ◯_{t}_{3}  4, 6  0, 2  s:4  ℚ(j)  2  (st)^{3}

G_{8}  A_{2}^{(4)}  ◯_{s}_{4}  ◯_{t}_{4}  8, 12  0, 4  s:6  ℚ(i)  4  (st)^{3}

G_{16}  A_{2}^{(5)}  ◯_{s}_{5}  ◯_{t}_{5}  20, 30  0, 10  s:12  ℚ(e^{2iπ/5}) 10  (st)^{3}

G_{25}  A_{3}^{(3)}  ◯_{s}_{3}  ◯_{t}_{3}  ◯_{u}_{3}  6, 9, 12  0, 3, 6  s:12  ℚ(j)  3  (stu)^{4}

G_{32}  A_{4}^{(3)}  ◯_{s}_{3} ◯_{t}_{3} ◯_{u}_{3} ◯_{v}_{3}  12, 18, 24, 30  0, 6, 12, 18  s:40  ℚ(j)  6  (stuv)^{5}

G(d, 1, r)_{d≥2} B_{r}^{(d)}  ◯_{t}_{d} ◯_{s_{2}} ◯_{s_{3}}⋯◯_{s_{r}}  [1, 2, …, r]d  [0, 1, …, r − 1]d t:r, s_{2}: \frac{r(r−1)}{2}d ℚ(e^{2iπ/d})  d  (ts_{2}s_{3} … s_{r})^{r}

G_{5}  B_{2}^{(3,3)}  ◯_{s}_{3}  ◯_{t}_{3}  6, 12  0, 6  s:4, t:4  ℚ(j)  6  (st)^{2}

G_{10}  B_{2}^{(4,3)}  ◯_{s}_{4}  ◯_{t}_{3}  12, 24  0, 12  s:6, t:8  ℚ(e^{2iπ/12}) 12  (st)^{2}

G_{26}  B_{3}^{(2,3)}  ◯_{s}  ◯_{t}_{3}  ◯_{u}_{3}  6, 12, 18  0, 6, 12  s:9, t:12  ℚ(j)  6  (stu)^{3}

G(2d, 2, r)_{d≥2} D_{r}^{(2d)} t◯ d  ^{◯^{s′_{2}}} ⧹_{◯_{s_{2}}} ⧸◯_{s_{3}} ◯_{s_{4}}⋯◯_{s_{r}} {[1, 2, …, r − 1]2d \atop rd} [0, 1, …, r − 1]2d t:r, s_{2}:r(r − 1)d ; {excepté r = 2: \atop t:2, s_{2} : d, s′_{2} : d} ℚ(e^{iπ/d}) d(2 ∧ r) t^{\frac{r}{2∧r}} (s′_{2}s_{2}s_{3} … s_{r})^{\frac{2(r−1)}{2∧r}}

G_{20}  I_{2}^{(3,3)}(5)  ◯_{s}_{3} ^{5} ◯_{t}_{3}  12, 30  0, 18  s:20  ℚ(j, \sqrt{5})  6  (st)^{5}

G_{9}  G_{2}^{(4)}  ◯_{s}_{4}  ◯_{t}  8, 24  0, 16  s:6, t:12  ℚ(e^{iπ/4})  8  (st)^{3}

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S&T Nom Diagramme Degrés Codegrés

Orbites d’hyperplans Corps

|ZW | β

G(e, e, 2)_{e≥3} I_{2}(e) ◯_{s} ^{e} ◯_{t} 2, e 0, e − 2 e pair s:e/2, t:e/2

e impair s:e ℚ(cos(2π/e)) e ∧ 2 (st)^{e/(e∧2)}

G_{12}  K_{2}  [figure: s; ◯; ◯t; ◯u]  6, 8  0, 10  s:12  ℚ(\sqrt{−2})  2  (stu)^{4}

G_{22}  M_{2}  s◯ 5 ^{◯t}_{◯u}  12, 20  0, 28  s:30  ℚ(i, \sqrt{5})  4  (stu)^{5}

G_{23}  H_{3}  ◯_{s} ^{5} ◯_{t}  ◯_{u}  2, 6, 10  0, 4, 8  s:15  ℚ(\sqrt{5})  2  (stu)^{5}

G_{28}  F_{4}  ◯_{s} ◯_{t} ◯_{u} ◯_{v}  2, 6, 8, 12  0, 4, 6, 10  s:12, t:12  ℚ  2  (stuv)^{6}

G_{30}  H_{4}  ◯_{s} ^{5} ◯_{t} ◯_{u} ◯_{v}  2, 12, 20, 30  0, 10, 18, 28  s:60  ℚ(\sqrt{5})  2  (stuv)^{15}

G_{31}  L_{4}  ◯_{v}⧸◯_{s} ◯_{t}  ◯_{w} ◯_{u}⧹  8, 12, 20, 24  0, 12, 16, 28  s:60  ℚ(i)  4  (stuwv)^{6}

G_{35}  E_{6}  ◯_{s_{1}} ◯_{s_{3}} ◯_{s_{4}}^{◯^{s_{2}}} ◯_{s_{5}} ◯_{s_{6}}  2, 5, 6, 8, 9, 12  0, 3, 4, 6, 7, 10  s:36  ℚ  1 (s_{1} … s_{6})^{12}

G_{36}  E_{7}  ◯_{s_{1}} ◯_{s_{3}} ◯_{s_{4}}^{◯^{s_{2}}} ◯_{s_{5}} ◯_{s_{6}} ◯_{s_{7}}  2, 6, 8, 10, 12, 14, 18  0, 4, 6, 8, 10, 12, 16  s:63  ℚ  2 (s_{1} … s_{7})^{9}

G_{37}  E_{8} ◯_{s_{1}} ◯_{s_{3}} ◯_{s_{4}}^{◯^{s_{2}}} ◯_{s_{5}} ◯_{s_{6}} ◯_{s_{7}} ◯_{s_{8}} 2, 8, 12, 14, 18, 20, 24, 30 0, 6, 10, 12, 16, 18, 22, 28  s:120  ℚ  2 (s_{1} … s_{8})^{15}