Overview
- Group
- SmallGroup(1600,10261)
- Rank
- 3
- Schläfli Type
- {5,20}
- Vertices, edges, …
- 40, 400, 160
- Order of s0s1s2
- 10
- Order of s0s1s2s1
- 20
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
5-fold
10-fold
16-fold
80-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 2
80 facets
- 80 of {5}*10
24 vertex figures
P/N, where N=<(s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2> of order 2
80 facets
- 80 of {5}*10
20 vertex figures
- 20 of {20}*40
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1> of order 2
80 facets
- 80 of {5}*10
20 vertex figures
- 20 of {20}*40
P/N, where N=<(s0*s1*s2*(s1*s0)^2*s2*s1)^2*s2> of order 2
80 facets
- 80 of {5}*10
20 vertex figures
- 20 of {20}*40
P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s0*s2> of order 2
80 facets
- 80 of {5}*10
20 vertex figures
- 20 of {20}*40
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1*s2> of order 2
80 facets
- 80 of {5}*10
20 vertex figures
- 20 of {20}*40
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2, s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 4
40 facets
- 40 of {5}*10
10 vertex figures
- 10 of {20}*40
P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s2> of order 4
40 facets
- 40 of {5}*10
10 vertex figures
- 10 of {20}*40
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1> of order 4
40 facets
- 40 of {5}*10
12 vertex figures
P/N, where N=<(s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2, (s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s0> of order 4
40 facets
- 40 of {5}*10
10 vertex figures
- 10 of {20}*40
P/N, where N=<(s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2*s2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1> of order 4
40 facets
- 40 of {5}*10
10 vertex figures
- 10 of {20}*40
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1, (s0*s1)^2*s0*(s2*s1)^2*s0*s2*(s1*s0)^2*(s2*s1)^2> of order 4
40 facets
- 40 of {5}*10
10 vertex figures
- 10 of {20}*40
P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*s0*(s1*s0*s2)^2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1> of order 4
40 facets
- 40 of {5}*10
12 vertex figures
P/N, where N=<(s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2, (s0*s1)^2*s2*(s1*s0)^2*(s2*s1*s0*s1)^2> of order 4
40 facets
- 40 of {5}*10
10 vertex figures
- 10 of {20}*40
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, (s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2> of order 4
40 facets
- 40 of {5}*10
10 vertex figures
- 10 of {20}*40
P/N, where N=<(s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2, (s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s0*s2> of order 4
40 facets
- 40 of {5}*10
10 vertex figures
- 10 of {20}*40
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1, s0*s1*s0*s2*s1*s0*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 4
40 facets
- 40 of {5}*10
14 vertex figures
P/N, where N=<(s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2, (s0*s1)^2*s2*(s1*s0)^2*(s2*s1*s0*s1)^2*s2> of order 4
40 facets
- 40 of {5}*10
14 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, (s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s0*s2> of order 4
40 facets
- 40 of {5}*10
12 vertex figures
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 4
40 facets
- 40 of {5}*10
12 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2> of order 4
40 facets
- 40 of {5}*10
12 vertex figures
P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s0*s2, (s0*s1)^2*s2*(s1*s0)^2*(s2*s1*s0*s1)^2> of order 4
40 facets
- 40 of {5}*10
12 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1> of order 4
40 facets
- 40 of {5}*10
10 vertex figures
- 10 of {20}*40
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s2> of order 8
20 facets
- 20 of {5}*10
6 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2, (s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s0> of order 8
20 facets
- 20 of {5}*10
8 vertex figures
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1)^2*s0*(s2*s1)^2*s0*(s1*s0*s2)^2> of order 8
20 facets
- 20 of {5}*10
8 vertex figures
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2, s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2, (s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2> of order 8
20 facets
- 20 of {5}*10
6 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, s0*s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 8
20 facets
- 20 of {5}*10
6 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2, (s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2, (s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s0*s2> of order 8
20 facets
- 20 of {5}*10
6 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, (s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2*s2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s0*s2)^2*s1> of order 8
20 facets
- 20 of {5}*10
7 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2, (s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2, (s0*s1)^2*s0*(s2*s1)^2*(s0*s2*s1)^2*s0*s2> of order 8
20 facets
- 20 of {5}*10
7 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14)(17,65)(18,66)(19,68)(20,67)(21,70)(22,69)(23,71)(24,72)(25,80)(26,79)(27,77)(28,78)(29,75)(30,76)(31,74)(32,73)(33,49)(34,50)(35,52)(36,51)(37,54)(38,53)(39,55)(40,56)(41,64)(42,63)(43,61)(44,62)(45,59)(46,60)(47,58)(48,57);; s1 := ( 1,17)( 2,26)( 3,27)( 4,20)( 5,32)( 6,23)( 7,22)( 8,29)( 9,25)(10,18)(11,19)(12,28)(13,24)(14,31)(15,30)(16,21)(33,65)(34,74)(35,75)(36,68)(37,80)(38,71)(39,70)(40,77)(41,73)(42,66)(43,67)(44,76)(45,72)(46,79)(47,78)(48,69)(50,58)(51,59)(53,64)(54,55)(56,61)(62,63);; s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,66)(18,65)(19,68)(20,67)(21,70)(22,69)(23,72)(24,71)(25,74)(26,73)(27,76)(28,75)(29,78)(30,77)(31,80)(32,79)(33,50)(34,49)(35,52)(36,51)(37,54)(38,53)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,62)(46,61)(47,64)(48,63);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(80)!( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14)(17,65)(18,66)(19,68)(20,67)(21,70)(22,69)(23,71)(24,72)(25,80)(26,79)(27,77)(28,78)(29,75)(30,76)(31,74)(32,73)(33,49)(34,50)(35,52)(36,51)(37,54)(38,53)(39,55)(40,56)(41,64)(42,63)(43,61)(44,62)(45,59)(46,60)(47,58)(48,57); s1 := Sym(80)!( 1,17)( 2,26)( 3,27)( 4,20)( 5,32)( 6,23)( 7,22)( 8,29)( 9,25)(10,18)(11,19)(12,28)(13,24)(14,31)(15,30)(16,21)(33,65)(34,74)(35,75)(36,68)(37,80)(38,71)(39,70)(40,77)(41,73)(42,66)(43,67)(44,76)(45,72)(46,79)(47,78)(48,69)(50,58)(51,59)(53,64)(54,55)(56,61)(62,63); s2 := Sym(80)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,66)(18,65)(19,68)(20,67)(21,70)(22,69)(23,72)(24,71)(25,74)(26,73)(27,76)(28,75)(29,78)(30,77)(31,80)(32,79)(33,50)(34,49)(35,52)(36,51)(37,54)(38,53)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,62)(46,61)(47,64)(48,63); poly := sub<Sym(80)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.