Great quasidisprismatohexacosihecatonicosachoron Rank 4 Type Uniform Notation Bowers style acronym Gaquidapixhi Coxeter diagram x5/3x3x3x ( ) Elements Cells 1200 hexagonal prisms , 720 decagrammic prisms , 600 truncated octahedra , 120 great quasitruncated icosidodecahedra Faces 3600+3600+3600 squares , 2400+2400 hexagons , 1440 decagrams Edges 7200+7200+7200+7200 Vertices 14400 Vertex figure Irregular tetrahedron , edge lengths √2 (3), √3 (2), and √(5–√5 )/2 (1)Measures (edge length 1) Circumradius
83
−
36
5
≈
1.58163
{\displaystyle {\sqrt {83-36{\sqrt {5}}}}\approx 1.58163}
Hypervolume
75
(
845
−
366
5
)
≈
1994.93402
{\displaystyle 75\left(845-366{\sqrt {5}}\right)\approx 1994.93402}
Dichoral angles Stiddip–4–hip:
arccos
(
−
10
−
2
5
15
)
≈
127.37737
∘
{\displaystyle \arccos \left(-{\sqrt {\frac {10-2{\sqrt {5}}}{15}}}\right)\approx 127.37737^{\circ }}
Gaquatid–10/3–stiddip: 126° Gaquatid–4–hip:
arccos
(
3
−
15
6
)
≈
110.95106
∘
{\displaystyle \arccos \left({\frac {{\sqrt {3}}-{\sqrt {15}}}{6}}\right)\approx 110.95106^{\circ }}
Gaquatid–6–toe:
arccos
(
7
−
3
5
4
)
≈
82.23876
∘
{\displaystyle \arccos \left({\frac {\sqrt {7-3{\sqrt {5}}}}{4}}\right)\approx 82.23876^{\circ }}
Toe–4–stiddip:
arccos
(
5
−
2
5
10
)
≈
76.71747
∘
{\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{10}}}\right)\approx 76.71747^{\circ }}
Toe–6–hip:
arccos
(
30
−
6
8
)
≈
67.76124
∘
{\displaystyle \arccos \left({\frac {{\sqrt {30}}-{\sqrt {6}}}{8}}\right)\approx 67.76124^{\circ }}
Central density 409 Number of external pieces 1616400 Level of complexity 6651 Related polytopes Army Semi-uniform Gidpixhi , edge lengths
9
−
4
5
{\displaystyle 9-4{\sqrt {5}}}
(squares of great rhombicosidodecahedra),
5
−
2
{\displaystyle {\sqrt {5}}-2}
(remaining edges of great rhombicosidodecahedra),
5
5
−
11
2
{\displaystyle {\frac {5{\sqrt {5}}-11}{2}}}
(edges not in great rhombicosidodecahedra)Regiment Gaquidapixhi Conjugate Great disprismatohexacosihecatonicosachoron Convex core Hexacosichoron Abstract & topological properties Flag count345600 Euler characteristic 0 Orientable Yes Properties Symmetry H4 , order 14400Convex No Nature Tame
The great quasidisprismatohexacosihecatonicosachoron , or gaquidapixhi , is a nonconvex uniform polychoron that consists of 1200 hexagonal prisms , 720 decagrammic prisms , 600 truncated octahedra , and 120 great quasitruncated icosidodecahedra . 1 of each type of cell join at each vertex. It is the quasiomnitruncate of the grand hexacosichoron and the great grand stellated hecatonicosachoron .
Vertex coordinates for a great quasidisprismatohexacosihecatonicosachoron of edge length 1 are given by all permutations of:
(
±
1
2
,
±
1
2
,
±
3
5
−
4
2
,
±
12
−
5
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {3{\sqrt {5}}-4}{2}},\,\pm {\frac {12-5{\sqrt {5}}}{2}}\right),}
(
±
1
2
,
±
1
2
,
±
4
5
−
7
2
,
±
11
−
4
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {4{\sqrt {5}}-7}{2}},\,\pm {\frac {11-4{\sqrt {5}}}{2}}\right),}
(
±
1
2
,
±
1
2
,
±
2
5
−
3
2
,
±
6
5
−
11
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {6{\sqrt {5}}-11}{2}}\right),}
(
±
1
2
,
±
3
2
,
±
9
−
4
5
2
,
±
9
−
4
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {3}{2}},\,\pm {\frac {9-4{\sqrt {5}}}{2}},\,\pm {\frac {9-4{\sqrt {5}}}{2}}\right),}
(
±
1
,
±
1
,
±
2
(
5
−
2
)
,
±
(
5
−
2
5
)
)
,
{\displaystyle \left(\pm 1,\,\pm 1,\,\pm 2({\sqrt {5}}-2),\,\pm (5-2{\sqrt {5}})\right),}
(
±
3
−
5
2
,
±
5
−
5
2
,
±
2
(
5
−
2
)
,
±
2
(
5
−
2
)
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {5-{\sqrt {5}}}{2}},\,\pm 2({\sqrt {5}}-2),\,\pm 2({\sqrt {5}}-2)\right),}
(
±
4
−
5
2
,
±
4
−
5
2
,
±
4
5
−
7
2
,
±
9
−
4
5
2
)
,
{\displaystyle \left(\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {4{\sqrt {5}}-7}{2}},\,\pm {\frac {9-4{\sqrt {5}}}{2}}\right),}
(
±
2
5
−
3
2
,
±
5
−
2
5
2
,
±
4
5
−
7
2
,
±
4
5
−
7
2
)
,
{\displaystyle \left(\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {5-2{\sqrt {5}}}{2}},\,\pm {\frac {4{\sqrt {5}}-7}{2}},\,\pm {\frac {4{\sqrt {5}}-7}{2}}\right),}
(
±
(
5
−
2
)
,
±
(
5
−
2
)
,
±
(
2
5
−
3
)
,
±
2
(
5
−
2
)
)
,
{\displaystyle \left(\pm ({\sqrt {5}}-2),\,\pm ({\sqrt {5}}-2),\,\pm (2{\sqrt {5}}-3),\,\pm 2({\sqrt {5}}-2)\right),}
plus all even permutations of:
(
±
1
2
,
±
5
3
−
5
4
,
±
7
5
−
15
4
,
±
3
3
−
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm 5{\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {7{\sqrt {5}}-15}{4}},\,\pm 3{\frac {3-{\sqrt {5}}}{2}}\right),}
(
±
1
2
,
±
7
−
3
5
2
,
±
17
−
7
5
4
,
±
17
−
5
5
4
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{2}},\,\pm {\frac {17-7{\sqrt {5}}}{4}},\,\pm {\frac {17-5{\sqrt {5}}}{4}}\right),}
(
±
1
2
,
±
1
,
±
5
5
−
7
4
,
±
11
5
−
23
4
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {5{\sqrt {5}}-7}{4}},\,\pm {\frac {11{\sqrt {5}}-23}{4}}\right),}
(
±
1
2
,
±
3
−
5
4
,
±
3
7
−
3
5
4
,
±
(
2
5
−
3
)
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm 3{\frac {7-3{\sqrt {5}}}{4}},\,\pm (2{\sqrt {5}}-3)\right),}
(
±
1
2
,
±
3
−
5
4
,
±
25
−
9
5
4
,
±
3
5
−
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {25-9{\sqrt {5}}}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{2}}\right),}
(
±
1
2
,
±
5
−
1
2
,
±
23
−
9
5
4
,
±
7
5
−
11
4
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {23-9{\sqrt {5}}}{4}},\,\pm {\frac {7{\sqrt {5}}-11}{4}}\right),}
(
±
1
2
,
±
5
−
2
2
,
±
6
5
−
11
2
,
±
4
−
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {6{\sqrt {5}}-11}{2}},\,\pm {\frac {4-{\sqrt {5}}}{2}}\right),}
(
±
1
2
,
±
7
−
5
4
,
±
9
5
−
17
4
,
±
2
(
5
−
2
)
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {7-{\sqrt {5}}}{4}},\,\pm {\frac {9{\sqrt {5}}-17}{4}},\,\pm 2({\sqrt {5}}-2)\right),}
(
±
1
2
,
±
3
5
−
5
4
,
±
25
−
9
5
4
,
±
(
3
−
5
)
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {25-9{\sqrt {5}}}{4}},\,\pm (3-{\sqrt {5}})\right),}
(
±
1
2
,
±
3
5
−
5
4
,
±
11
5
−
23
4
,
±
5
−
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {11{\sqrt {5}}-23}{4}},\,\pm {\frac {5-{\sqrt {5}}}{2}}\right),}
(
±
1
2
,
±
(
5
−
1
)
,
±
23
−
9
5
4
,
±
13
−
5
5
4
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm ({\sqrt {5}}-1),\,\pm {\frac {23-9{\sqrt {5}}}{4}},\,\pm {\frac {13-5{\sqrt {5}}}{4}}\right),}
(
±
1
2
,
±
3
3
−
5
4
,
±
9
5
−
17
4
,
±
3
3
−
5
2
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm 3{\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {9{\sqrt {5}}-17}{4}},\,\pm 3{\frac {3-{\sqrt {5}}}{2}}\right),}
(
±
1
2
,
±
(
5
−
2
)
,
±
9
5
−
19
4
,
±
17
−
5
5
4
)
,
{\displaystyle \left(\pm {\frac {1}{2}},\,\pm ({\sqrt {5}}-2),\,\pm {\frac {9{\sqrt {5}}-19}{4}},\,\pm {\frac {17-5{\sqrt {5}}}{4}}\right),}
(
±
1
,
±
3
−
5
4
,
±
6
5
−
11
2
,
±
7
−
3
5
4
)
,
{\displaystyle \left(\pm 1,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {6{\sqrt {5}}-11}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{4}}\right),}
(
±
1
,
±
5
−
5
4
,
±
9
5
−
19
4
,
±
4
5
−
7
2
)
,
{\displaystyle \left(\pm 1,\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {9{\sqrt {5}}-19}{4}},\,\pm {\frac {4{\sqrt {5}}-7}{2}}\right),}
(
±
1
,
±
5
−
2
2
,
±
25
−
9
5
4
,
±
5
5
−
11
4
)
,
{\displaystyle \left(\pm 1,\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {25-9{\sqrt {5}}}{4}},\,\pm {\frac {5{\sqrt {5}}-11}{4}}\right),}
(
±
1
,
±
3
5
−
1
4
,
±
23
−
9
5
4
,
±
3
5
−
2
2
)
,
{\displaystyle \left(\pm 1,\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {23-9{\sqrt {5}}}{4}},\,\pm 3{\frac {{\sqrt {5}}-2}{2}}\right),}
(
±
1
,
±
3
5
−
5
4
,
±
12
−
5
5
2
,
±
11
−
3
5
4
)
,
{\displaystyle \left(\pm 1,\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {12-5{\sqrt {5}}}{2}},\,\pm {\frac {11-3{\sqrt {5}}}{4}}\right),}
(
±
1
,
±
4
−
5
2
,
±
9
5
−
17
4
,
±
17
−
7
5
4
)
,
{\displaystyle \left(\pm 1,\,\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {9{\sqrt {5}}-17}{4}},\,\pm {\frac {17-7{\sqrt {5}}}{4}}\right),}
(
±
1
,
±
2
5
−
3
2
,
±
3
7
−
3
5
4
,
±
5
3
−
5
4
)
,
{\displaystyle \left(\pm 1,\,\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm 3{\frac {7-3{\sqrt {5}}}{4}},\,\pm 5{\frac {3-{\sqrt {5}}}{4}}\right),}
(
±
3
−
5
4
,
±
13
−
5
5
4
,
±
4
5
−
7
2
,
±
3
3
−
5
2
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {13-5{\sqrt {5}}}{4}},\,\pm {\frac {4{\sqrt {5}}-7}{2}},\,\pm 3{\frac {3-{\sqrt {5}}}{2}}\right),}
(
±
3
−
5
4
,
±
3
5
−
2
2
,
±
2
(
5
−
2
)
,
±
17
−
5
5
4
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm 3{\frac {{\sqrt {5}}-2}{2}},\,\pm 2({\sqrt {5}}-2),\,\pm {\frac {17-5{\sqrt {5}}}{4}}\right),}
(
±
3
−
5
4
,
±
3
2
,
±
(
5
−
2
)
,
±
11
5
−
23
4
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {3}{2}},\,\pm ({\sqrt {5}}-2),\,\pm {\frac {11{\sqrt {5}}-23}{4}}\right),}
(
±
3
−
5
4
,
±
3
5
−
1
4
,
±
6
5
−
11
2
,
±
3
−
5
2
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {6{\sqrt {5}}-11}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}}\right),}
(
±
3
−
5
4
,
±
4
−
5
2
,
±
(
5
−
1
)
,
±
11
5
−
23
4
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm ({\sqrt {5}}-1),\,\pm {\frac {11{\sqrt {5}}-23}{4}}\right),}
(
±
3
−
5
4
,
±
11
−
3
5
4
,
±
9
−
4
5
2
,
±
3
3
−
5
2
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {11-3{\sqrt {5}}}{4}},\,\pm {\frac {9-4{\sqrt {5}}}{2}},\,\pm 3{\frac {3-{\sqrt {5}}}{2}}\right),}
(
±
3
−
5
4
,
±
5
−
2
5
2
,
±
(
5
−
2
5
)
,
±
17
−
5
5
4
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {5-2{\sqrt {5}}}{2}},\,\pm (5-2{\sqrt {5}}),\,\pm {\frac {17-5{\sqrt {5}}}{4}}\right),}
(
±
3
2
,
±
5
−
2
2
,
±
12
−
5
5
2
,
±
5
−
2
5
2
)
,
{\displaystyle \left(\pm {\frac {3}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {12-5{\sqrt {5}}}{2}},\,\pm {\frac {5-2{\sqrt {5}}}{2}}\right),}
(
±
3
2
,
±
3
−
5
2
,
±
9
5
−
19
4
,
±
7
5
−
15
4
)
,
{\displaystyle \left(\pm {\frac {3}{2}},\,\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {9{\sqrt {5}}-19}{4}},\,\pm {\frac {7{\sqrt {5}}-15}{4}}\right),}
(
±
3
2
,
±
3
5
−
5
4
,
±
3
7
−
3
5
4
,
±
7
−
3
5
2
)
,
{\displaystyle \left(\pm {\frac {3}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm 3{\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {7-3{\sqrt {5}}}{2}}\right),}
(
±
5
−
1
2
,
±
(
3
−
5
)
,
±
2
(
5
−
2
)
,
±
3
3
−
5
2
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm (3-{\sqrt {5}}),\,\pm 2({\sqrt {5}}-2),\,\pm 3{\frac {3-{\sqrt {5}}}{2}}\right),}
(
±
5
−
1
2
,
±
5
5
−
11
4
,
±
9
−
4
5
2
,
±
17
−
5
5
4
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {5{\sqrt {5}}-11}{4}},\,\pm {\frac {9-4{\sqrt {5}}}{2}},\,\pm {\frac {17-5{\sqrt {5}}}{4}}\right),}
(
±
5
−
1
2
,
±
5
−
5
4
,
±
3
5
−
5
4
,
±
6
5
−
11
2
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {6{\sqrt {5}}-11}{2}}\right),}
(
±
5
−
1
2
,
,
±
7
−
5
4
,
±
2
5
−
3
2
,
±
11
5
−
23
4
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {5}}-1}{2}},,\,\pm {\frac {7-{\sqrt {5}}}{4}},\,\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {11{\sqrt {5}}-23}{4}}\right),}
(
±
5
−
5
4
,
±
(
5
−
1
)
,
±
12
−
5
5
2
,
±
3
3
−
5
4
)
,
{\displaystyle \left(\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm ({\sqrt {5}}-1),\,\pm {\frac {12-5{\sqrt {5}}}{2}},\,\pm 3{\frac {3-{\sqrt {5}}}{4}}\right),}
(
±
5
−
5
4
,
±
5
−
5
2
,
±
9
−
4
5
2
,
±
17
−
7
5
4
)
,
{\displaystyle \left(\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {5-{\sqrt {5}}}{2}},\,\pm {\frac {9-4{\sqrt {5}}}{2}},\,\pm {\frac {17-7{\sqrt {5}}}{4}}\right),}
(
±
5
−
5
4
,
±
(
5
−
2
)
,
±
11
−
4
5
2
,
±
5
3
−
5
4
)
,
{\displaystyle \left(\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm ({\sqrt {5}}-2),\,\pm {\frac {11-4{\sqrt {5}}}{2}},\,\pm 5{\frac {3-{\sqrt {5}}}{4}}\right),}
(
±
5
−
2
2
,
±
13
−
5
5
4
,
±
(
2
5
−
3
)
,
±
17
−
7
5
4
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {13-5{\sqrt {5}}}{4}},\,\pm (2{\sqrt {5}}-3),\,\pm {\frac {17-7{\sqrt {5}}}{4}}\right),}
(
±
5
−
2
2
,
±
5
3
−
5
4
,
±
7
5
−
11
4
,
±
2
(
5
−
2
)
)
,
{\displaystyle \left(\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm 5{\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {7{\sqrt {5}}-11}{4}},\,\pm 2({\sqrt {5}}-2)\right),}
(
±
7
−
5
4
,
±
3
5
−
1
4
,
±
12
−
5
5
2
,
±
(
5
−
2
)
)
,
{\displaystyle \left(\pm {\frac {7-{\sqrt {5}}}{4}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {12-5{\sqrt {5}}}{2}},\,\pm ({\sqrt {5}}-2)\right),}
(
±
7
−
5
4
,
±
4
−
5
2
,
±
(
5
−
2
5
)
,
±
7
5
−
15
4
)
,
{\displaystyle \left(\pm {\frac {7-{\sqrt {5}}}{4}},\,\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm (5-2{\sqrt {5}}),\,\pm {\frac {7{\sqrt {5}}-15}{4}}\right),}
(
±
7
−
5
4
,
±
7
−
3
5
4
,
±
11
−
4
5
2
,
±
7
−
3
5
2
)
,
{\displaystyle \left(\pm {\frac {7-{\sqrt {5}}}{4}},\,\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {11-4{\sqrt {5}}}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{2}}\right),}
(
±
3
5
−
1
4
,
±
(
3
−
5
)
,
±
4
5
−
7
2
,
±
17
−
7
5
4
)
,
{\displaystyle \left(\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm (3-{\sqrt {5}}),\,\pm {\frac {4{\sqrt {5}}-7}{2}},\,\pm {\frac {17-7{\sqrt {5}}}{4}}\right),}
(
±
3
5
−
1
4
,
±
3
5
−
5
2
,
±
9
−
4
5
2
,
±
5
3
−
5
4
)
,
{\displaystyle \left(\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{2}},\,\pm {\frac {9-4{\sqrt {5}}}{2}},\,\pm 5{\frac {3-{\sqrt {5}}}{4}}\right),}
(
±
3
−
5
2
,
±
2
5
−
3
2
,
±
25
−
9
5
4
,
±
3
3
−
5
4
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {25-9{\sqrt {5}}}{4}},\,\pm 3{\frac {3-{\sqrt {5}}}{4}}\right),}
(
±
3
−
5
2
,
±
5
5
−
7
4
,
±
11
−
4
5
2
,
±
13
−
5
5
4
)
,
{\displaystyle \left(\pm {\frac {3-{\sqrt {5}}}{2}},\,\pm {\frac {5{\sqrt {5}}-7}{4}},\,\pm {\frac {11-4{\sqrt {5}}}{2}},\,\pm {\frac {13-5{\sqrt {5}}}{4}}\right),}
(
±
3
5
−
5
4
,
±
3
5
−
4
2
,
±
(
5
−
2
5
)
,
±
13
−
5
5
4
)
,
{\displaystyle \left(\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {3{\sqrt {5}}-4}{2}},\,\pm (5-2{\sqrt {5}}),\,\pm {\frac {13-5{\sqrt {5}}}{4}}\right),}
(
±
3
5
−
5
4
,
±
3
5
−
2
2
,
±
(
2
5
−
3
)
,
±
7
5
−
15
4
)
,
{\displaystyle \left(\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm 3{\frac {{\sqrt {5}}-2}{2}},\,\pm (2{\sqrt {5}}-3),\,\pm {\frac {7{\sqrt {5}}-15}{4}}\right),}
(
±
3
5
−
5
4
,
±
7
5
−
11
4
,
±
4
5
−
7
2
,
±
7
−
3
5
2
)
,
{\displaystyle \left(\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {7{\sqrt {5}}-11}{4}},\,\pm {\frac {4{\sqrt {5}}-7}{2}},\,\pm {\frac {7-3{\sqrt {5}}}{2}}\right),}
(
±
3
5
−
5
4
,
±
4
−
5
2
,
±
(
5
−
2
)
,
±
25
−
9
5
4
)
,
{\displaystyle \left(\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm ({\sqrt {5}}-2),\,\pm {\frac {25-9{\sqrt {5}}}{4}}\right),}
(
±
3
5
−
5
4
,
±
11
−
3
5
4
,
±
4
5
−
7
2
,
±
2
(
5
−
2
)
)
,
{\displaystyle \left(\pm {\frac {3{\sqrt {5}}-5}{4}},\,\pm {\frac {11-3{\sqrt {5}}}{4}},\,\pm {\frac {4{\sqrt {5}}-7}{2}},\,\pm 2({\sqrt {5}}-2)\right),}
(
±
4
−
5
2
,
±
2
5
−
3
2
,
±
11
−
4
5
2
,
±
3
5
−
2
2
)
,
{\displaystyle \left(\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {11-4{\sqrt {5}}}{2}},\,\pm 3{\frac {{\sqrt {5}}-2}{2}}\right),}
(
±
4
−
5
2
,
±
(
5
−
2
)
,
±
23
−
9
5
4
,
±
11
−
3
5
4
)
,
{\displaystyle \left(\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm ({\sqrt {5}}-2),\,\pm {\frac {23-9{\sqrt {5}}}{4}},\,\pm {\frac {11-3{\sqrt {5}}}{4}}\right),}
(
±
4
−
5
2
,
±
5
5
−
7
4
,
±
3
7
−
3
5
4
,
±
(
3
−
5
)
)
,
{\displaystyle \left(\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {5{\sqrt {5}}-7}{4}},\,\pm 3{\frac {7-3{\sqrt {5}}}{4}},\,\pm (3-{\sqrt {5}})\right),}
(
±
(
5
−
1
)
,
±
5
5
−
11
4
,
±
4
5
−
7
2
,
±
7
5
−
15
4
)
,
{\displaystyle \left(\pm ({\sqrt {5}}-1),\,\pm {\frac {5{\sqrt {5}}-11}{4}},\,\pm {\frac {4{\sqrt {5}}-7}{2}},\,\pm {\frac {7{\sqrt {5}}-15}{4}}\right),}
(
±
(
5
−
1
)
,
±
3
5
−
5
2
,
±
2
(
5
−
2
)
,
±
7
−
3
5
2
)
,
{\displaystyle \left(\pm ({\sqrt {5}}-1),\,\pm {\frac {3{\sqrt {5}}-5}{2}},\,\pm 2({\sqrt {5}}-2),\,\pm {\frac {7-3{\sqrt {5}}}{2}}\right),}
(
±
7
−
3
5
4
,
±
(
3
−
5
)
,
±
3
5
−
4
2
,
±
9
5
−
19
4
)
,
{\displaystyle \left(\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm (3-{\sqrt {5}}),\,\pm {\frac {3{\sqrt {5}}-4}{2}},\,\pm {\frac {9{\sqrt {5}}-19}{4}}\right),}
(
±
7
−
3
5
4
,
±
5
−
5
2
,
±
5
−
2
5
2
,
±
23
−
9
5
4
)
,
{\displaystyle \left(\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {5-{\sqrt {5}}}{2}},\,\pm {\frac {5-2{\sqrt {5}}}{2}},\,\pm {\frac {23-9{\sqrt {5}}}{4}}\right),}
(
±
7
−
3
5
4
,
±
3
3
−
5
4
,
±
(
2
5
−
3
)
,
±
9
−
4
5
2
)
,
{\displaystyle \left(\pm {\frac {7-3{\sqrt {5}}}{4}},\,\pm 3{\frac {3-{\sqrt {5}}}{4}},\,\pm (2{\sqrt {5}}-3),\,\pm {\frac {9-4{\sqrt {5}}}{2}}\right),}
(
±
5
−
5
2
,
±
2
5
−
3
2
,
±
3
7
−
3
5
4
,
±
5
5
−
11
4
)
,
{\displaystyle \left(\pm {\frac {5-{\sqrt {5}}}{2}},\,\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm 3{\frac {7-3{\sqrt {5}}}{4}},\,\pm {\frac {5{\sqrt {5}}-11}{4}}\right),}
(
±
2
5
−
3
2
,
±
3
5
−
4
2
,
±
9
−
4
5
2
,
±
3
5
−
2
2
)
,
{\displaystyle \left(\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {3{\sqrt {5}}-4}{2}},\,\pm {\frac {9-4{\sqrt {5}}}{2}},\,\pm 3{\frac {{\sqrt {5}}-2}{2}}\right),}
(
±
2
5
−
3
2
,
±
3
3
−
5
4
,
±
7
5
−
11
4
,
±
(
5
−
2
5
)
)
,
{\displaystyle \left(\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm 3{\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {7{\sqrt {5}}-11}{4}},\,\pm (5-2{\sqrt {5}})\right),}
(
±
2
5
−
3
2
,
±
11
−
3
5
4
,
±
3
5
−
5
2
,
±
9
5
−
19
4
)
,
{\displaystyle \left(\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {11-3{\sqrt {5}}}{4}},\,\pm {\frac {3{\sqrt {5}}-5}{2}},\,\pm {\frac {9{\sqrt {5}}-19}{4}}\right),}
(
±
(
5
−
2
)
,
±
3
5
−
4
2
,
±
9
5
−
17
4
,
±
5
5
−
11
4
)
,
{\displaystyle \left(\pm ({\sqrt {5}}-2),\,\pm {\frac {3{\sqrt {5}}-4}{2}},\,\pm {\frac {9{\sqrt {5}}-17}{4}},\,\pm {\frac {5{\sqrt {5}}-11}{4}}\right),}
(
±
(
5
−
2
)
,
±
5
5
−
7
4
,
±
9
−
4
5
2
,
±
7
5
−
11
4
)
,
{\displaystyle \left(\pm ({\sqrt {5}}-2),\,\pm {\frac {5{\sqrt {5}}-7}{4}},\,\pm {\frac {9-4{\sqrt {5}}}{2}},\,\pm {\frac {7{\sqrt {5}}-11}{4}}\right),}
(
±
5
5
−
7
4
,
±
5
−
2
5
2
,
±
3
5
−
5
2
,
±
9
5
−
17
4
)
.
{\displaystyle \left(\pm {\frac {5{\sqrt {5}}-7}{4}},\,\pm {\frac {5-2{\sqrt {5}}}{2}},\,\pm {\frac {3{\sqrt {5}}-5}{2}},\,\pm {\frac {9{\sqrt {5}}-17}{4}}\right).}