Great quasidisprismatohecatonicosihecatonicosachoron

Great quasidisprismatohecatonicosihecatonicosachoron
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gaquidphihi
Coxeter diagram	x5/3x3x5x ()
Elements
Cells	720 decagonal prisms, 720 decagrammic prisms, 120 great rhombicosidodecahedra, 120 great quasitruncated icosidodecahedra
Faces	3600+3600+3600 squares, 2400 hexagons, 1440 decagons, 1440 decagrams
Edges	7200+7200+7200+7200
Vertices	14400
Vertex figure	Irregular tetrahedron, edge lengths √2 (3), √3 (1), √(5+√5)/2 (1), and √(5–√5)/2 (1)
Measures (edge length 1)
Circumradius	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3\sqrt2 \approx 4.24264}
Hypervolume	2850
Dichoral angles	Gaquatid–10/3–stiddip: 162°
	Dip–4–stiddip: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \arccos\left(-\frac{2\sqrt5}{5}\right) \approx 153.43495^\circ}
	Grid–10–dip: 126°
	Gaquatid–6–grid: 60°
	Grid–4–stiddip: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \arccos\left(\sqrt{\frac{5-\sqrt5}{10}}\right) \approx 58.28253^\circ}
	Gaquatid–4–dip: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \arccos\left(\sqrt{\frac{5+\sqrt5}{10}}\right) \approx 31.71747^\circ}
Number of external pieces	105240
Level of complexity	363
Related polytopes
Army	Semi-uniform Gidpixhi, edge lengths Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3-\sqrt5}{2}} (sides of ditrigonal prisms), Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt5-2} (remaining edges of dipentagons), Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{7-3\sqrt5}{2}} (non-dipentagonal edges of great rhombicosidodecahedra)), Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3\sqrt5-5}{2}} (edges not in great rhombicosidodecahedra)
Regiment	Gaquidphihi
Conjugate	Great quasidisprismatohecatonicosihecatonicosachoron
Convex core	Hecatonicosachoron
Abstract & topological properties
Flag count	345600
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great quasidisprismatohecatonicosihecatonicosachoron, or gaquidphihi, is a nonconvex uniform polychoron that consists of 720 decagonal prisms, 720 decagrammic prisms, 120 great rhombicosidodecahedron, and 120 great quasitruncated icosidodecahedra. 1 of each type of cell join at each vertex. It is the quasiomnitruncate of the grand hecatonicosachoron and the great stellated hecatonicosachoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

Vertex coordinates for a great quasidisprismatohecatonicosihecatonicosachoron of edge length 1 are given by all permutations of:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3\sqrt5-5}{4},\,\pm \frac{3\sqrt5-5}{4},\,\pm 3\frac{1+\sqrt5}{4},\,\pm \frac{7+3\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm \frac12,\,\pm \frac{2\sqrt5-3}{2},\,\pm \frac{6+\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm \frac12,\,\pm \frac{6-\sqrt5}{2},\,\pm \frac{3+2\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm \frac12,\,\pm \frac52,\,\pm \frac{3\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm 3\frac{\sqrt5-1}{4},\,\pm 3\frac{\sqrt5-1}{4},\,\pm \frac{7+\sqrt5}{4},\,\pm \frac{11+\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{9-\sqrt5}{4},\,\pm \frac{9-\sqrt5}{4},\,\pm \frac{1+3\sqrt5}{4},\,\pm \frac{5+3\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm 3\frac{1+\sqrt5}{4},\,\pm 3\frac{1+\sqrt5}{4},\,\pm \frac{7-\sqrt5}{4},\,\pm \frac{11-\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{5+3\sqrt5}{4},\,\pm \frac{5+3\sqrt5}{4},\,\pm \frac{7-3\sqrt5}{4},\,\pm 3\frac{\sqrt5-1}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{9+\sqrt5}{4},\,\pm \frac{9+\sqrt5}{4},\,\pm \frac{3\sqrt5-5}{4},\,\pm \frac{3\sqrt5-1}{4}\right),}

Plus all even permutations of:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{7-3\sqrt5}{4},\,\pm \frac{3-\sqrt5}{4},\,\pm 1,\,\pm \frac{6+\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{7-3\sqrt5}{4},\,\pm \frac{\sqrt5-1}{2},\,\pm \frac{4+\sqrt5}{2},\,\pm \frac{9+\sqrt55}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{7-3\sqrt5}{4},\,\pm \frac{7-\sqrt5}{4},\,\pm \frac{1+\sqrt5}{2},\,\pm \frac{3+2\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{7-3\sqrt5}{4},\,\pm \frac{3+\sqrt5}{4},\,\pm \frac{1+3\sqrt5}{4},\,\pm \frac{3+5\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{\sqrt5-2}{2},\,\pm \frac{3\sqrt5-5}{4},\,\pm \frac{11+\sqrt5}{4},\,\pm \frac{3+\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{\sqrt5-2}{2},\,\pm \frac12,\,\pm \frac{4-\sqrt5}{2},\,\pm \frac{6+\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{\sqrt5-2}{2},\,\pm \frac{7-\sqrt5}{4},\,\pm \frac{3+\sqrt5}{4},\,\pm \frac{1+3\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{\sqrt5-2}{2},\,\pm (\sqrt5-1),\,\pm \frac{9+\sqrt5}{4},\,\pm \frac{5+3\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{\sqrt5-2}{2},\,\pm \frac32,\,\pm \frac{2+\sqrt5}{2},\,\pm \frac{3\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{4},\,\pm \frac{3-\sqrt5}{2},\,\pm 3\frac{\sqrt5-1}{4},\,\pm \frac{6+\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{4},\,\pm \frac{3\sqrt5-5}{4},\,\pm \frac{13+\sqrt5}{4},\,\pm \frac{5+\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{4},\,\pm \frac12,\,\pm \frac{1+3\sqrt5}{2},\,\pm \frac{9-\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{4},\,\pm \frac12,\,\pm (1+\sqrt5),\,\pm \frac{13-\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{4},\,\pm \frac{\sqrt5}{2},\,\pm \frac{3\sqrt5-1}{2},\,\pm \frac{5+3\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{4},\,\pm \frac{7-\sqrt5}{4},\,\pm \frac{3\sqrt5-1}{4},\,\pm \frac{13+\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{4},\,\pm \frac{3\sqrt5-1}{4},\,\pm \frac{5\sqrt5-3}{4},\,\pm \frac{7+3\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{4},\,\pm \frac{5\sqrt5-3}{4},\,\pm \frac{9+\sqrt5}{4},\,\pm 3\frac{1+\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{4},\,\pm \frac{2+\sqrt5}{2},\,\pm \frac{3\sqrt5-1}{2},\,\pm \frac{7+\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{2},\,\pm \frac{3\sqrt5-5}{4},\,\pm \frac{3+2\sqrt5}{2},\,\pm \frac{9-\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{2},\,\pm \frac{\sqrt5-1}{2},\,\pm \frac{1+3\sqrt5}{2},\,\pm \frac{1+\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{2},\,\pm \frac{2+\sqrt5}{2},\,\pm \frac{5+3\sqrt5}{4},\,\pm \frac{11-\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5}{2},\,\pm \frac{1+3\sqrt5}{4},\,\pm \frac{9+\sqrt5}{4},\,\pm \frac52\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3\sqrt5-5}{4},\,\pm \frac12,\,\pm \sqrt5,\,\pm \frac{3+5\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3-\sqrt5-5}{4},\,\pm \frac{\sqrt5-1}{2},\,\pm \frac{5-\sqrt5}{4},\,\pm \frac{6+\sqrt5}{2}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3\sqrt5-5}{4},\,\pm \frac{\sqrt5}{2},\,\pm \frac{1+3\sqrt5}{2},\,\pm \frac{3+\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac{3\sqrt5-5}{4},\,\pm \frac{9-\sqrt5}{4},\,\pm \frac{2+\sqrt5}{2},\,\pm (1+\sqrt5)\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm \frac{\sqrt5-1}{2},\,\pm \frac{11-\sqrt5}{4},\,\pm \frac{3+5\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm \frac{\sqrt5-1}{2},\,\pm \frac{13+\sqrt5}{4},\,\pm \frac{9-\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm 3\frac{\sqrt5-1}{4},\,\pm \frac{1+3\sqrt5}{2},\,\pm \frac{3\sqrt5-1}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm (\sqrt5-1),\,\pm \frac{13+\sqrt5}{4},\,\pm \frac{3+\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm \frac{3+\sqrt5}{4},\,\pm \frac{1+3\sqrt5}{2},\,\pm \frac{9+\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm \frac{1+\sqrt5}{2},\,\pm \frac{5\sqrt5-3}{4},\,\pm \frac{11+\sqrt5}{4}\right),}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left(\pm \frac12,\,\pm \frac{1+\sqrt5}{2},\,\pm \frac{9+\sqrt5}{4},\,\pm \frac{13-\sqrt5}{4}\right),}
$\left(\pm {\frac {1}{2}},\,\pm {\frac {6-{\sqrt {5}}}{2}},\,\pm {\frac {2+{\sqrt {5}}}{2}},\,\pm {\frac {4+{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm {\frac {3{\sqrt {5}}-1}{2}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {1}{2}},\,\pm {\frac {5{\sqrt {5}}-3}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\sqrt {5}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {3{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {13+{\sqrt {5}}}{4}},\,\pm {\frac {3}{2}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3{\sqrt {5}}-1}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {{\sqrt {5}}-1}{2}},\,\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm {\frac {5{\sqrt {5}}-1}{4}},\,\pm {\frac {4+{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm ({\sqrt {5}}-1),\,\pm {\frac {3+2{\sqrt {5}}}{2}},\,\pm {\frac {3{\sqrt {5}}-1}{4}}\right),$
$\left(\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {13-{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {5-{\sqrt {5}}}{4}},\,\pm {\frac {9-{\sqrt {5}}}{4}},\,\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm {\frac {11+{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {3+2{\sqrt {5}}}{2}},\,\pm {\frac {3}{2}}\right),$
$\left(\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {3{\sqrt {5}}-1}{4}},\,\pm {\frac {5+3{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {2{\sqrt {5}}-3}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm (1+{\sqrt {5}})\right),$
$\left(\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm (1+{\sqrt {5}}),\,\pm 3{\frac {1+{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm {\frac {5}{2}}\right),$
$\left(\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {3{\sqrt {5}}-1}{4}},\,\pm {\frac {3+5{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {4-{\sqrt {5}}}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {9-{\sqrt {5}}}{4}}\right),$
$\left(\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm ({\sqrt {5}}-1),\,\pm {\frac {4+{\sqrt {5}}}{2}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}}\right),$
$\left(\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3+5{\sqrt {5}}}{4}},\,\pm {\frac {9-{\sqrt {5}}}{4}}\right),$
$\left(\pm 3{\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {3{\sqrt {5}}}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}}\right),$
$\left(\pm 1,\,\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {11+{\sqrt {5}}}{4}},\,\pm {\frac {11-{\sqrt {5}}}{4}}\right),$
$\left(\pm 1,\,\pm ({\sqrt {5}}-1),\,\pm (1+{\sqrt {5}}),\,\pm {\sqrt {5}}\right),$
$\left(\pm 1,\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {7+3{\sqrt {5}}}{4}},\,\pm {\frac {6-{\sqrt {5}}}{2}}\right),$
$\left(\pm 1,\,\pm {\frac {3{\sqrt {5}}-1}{4}},\,\pm {\frac {3{\sqrt {5}}}{2}},\,\pm {\frac {1+3{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {6-{\sqrt {5}}}{2}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {7-{\sqrt {5}}}{4}},\,\pm {\sqrt {5}},\,\pm {\frac {9+{\sqrt {5}}}{4}},\,\pm {\frac {5}{2}}\right),$
$\left(\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1+3{\sqrt {5}}}{4}},\,\pm {\frac {7+{\sqrt {5}}}{4}},\,\pm {\frac {13-{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {3{\sqrt {5}}-1}{4}},\,\pm {\frac {9-{\sqrt {5}}}{4}},\,\pm {\frac {5}{2}},\,\pm {\frac {3+{\sqrt {5}}}{2}}\right),$
$\left(\pm {\frac {3{\sqrt {5}}-1}{4}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {11-{\sqrt {5}}}{4}},\,\pm {\frac {9+{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {3}{2}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm 3{\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {13-{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {3}{2}},\,\pm {\frac {9-{\sqrt {5}}}{4}},\,\pm {\sqrt {5}},\,\pm {\frac {9+{\sqrt {5}}}{4}}\right),$
$\left(\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {6-{\sqrt {5}}}{2}},\,\pm {\frac {5+3{\sqrt {5}}}{4}}\right).$