Overview
- Group
- SmallGroup(1600,10261)
- Rank
- 3
- Schläfli Type
- {20,5}
- Vertices, edges, …
- 160, 400, 40
- 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)^2)^2> of order 2
20 facets
- 20 of {20}*40
80 vertex figures
- 80 of {5}*10
P/N, where N=<s1*(s2*s1*s0)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 2
20 facets
- 20 of {20}*40
80 vertex figures
- 80 of {5}*10
P/N, where N=<(s0*s1)^2*s2*s1*s0*(s2*s1)^2*s0*s1*s2*s1*s0*s2*s1*s2> of order 2
20 facets
- 20 of {20}*40
80 vertex figures
- 80 of {5}*10
P/N, where N=<s0*(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2> of order 2
20 facets
- 20 of {20}*40
80 vertex figures
- 80 of {5}*10
P/N, where N=<s0*s1*s0*s2*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 2
20 facets
- 20 of {20}*40
80 vertex figures
- 80 of {5}*10
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 4
12 facets
40 vertex figures
- 40 of {5}*10
P/N, where N=<s0*(s1*s0*s2)^2*(s1*s0)^2*(s1*s2)^2*s1> of order 4
10 facets
- 10 of {20}*40
40 vertex figures
- 40 of {5}*10
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2, s1*(s2*s1*s0)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 4
12 facets
40 vertex figures
- 40 of {5}*10
P/N, where N=<s1*s0*s1*s2*s1*s0*s1*(s2*s1*s0)^2*s2*s1> of order 4
12 facets
40 vertex figures
- 40 of {5}*10
P/N, where N=<s1*(s2*s1*s0)^2*s2*(s1*s0)^2*(s1*s2)^2, (s0*s1*s2*s1)^2*s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
14 facets
40 vertex figures
- 40 of {5}*10
P/N, where N=<s1*(s2*s1*s0)^2*s2*(s1*s0)^2*(s1*s2)^2, (s1*s2*s1*s0)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 4
10 facets
- 10 of {20}*40
40 vertex figures
- 40 of {5}*10
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 4
10 facets
- 10 of {20}*40
40 vertex figures
- 40 of {5}*10
P/N, where N=<(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2, s1*s0*s2*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 4
10 facets
- 10 of {20}*40
40 vertex figures
- 40 of {5}*10
P/N, where N=<s0*(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2, s1*(s2*s1*s0)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 4
10 facets
- 10 of {20}*40
40 vertex figures
- 40 of {5}*10
P/N, where N=<s0*(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2, (s1*s2*s1*s0)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 4
12 facets
40 vertex figures
- 40 of {5}*10
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, s0*(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2> of order 4
12 facets
40 vertex figures
- 40 of {5}*10
P/N, where N=<s0*s1*s0*s2*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2, (s1*s0*(s2*s1)^2*s0*s1*s2)^2> of order 4
12 facets
40 vertex figures
- 40 of {5}*10
P/N, where N=<s0*(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2, s1*s0*s2*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 4
10 facets
- 10 of {20}*40
40 vertex figures
- 40 of {5}*10
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1*s0*(s2*s1)^2)^2> of order 4
10 facets
- 10 of {20}*40
40 vertex figures
- 40 of {5}*10
P/N, where N=<(s0*s1*s0*(s2*s1)^2)^2, s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 4
12 facets
40 vertex figures
- 40 of {5}*10
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2, s0*(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2> of order 4
10 facets
- 10 of {20}*40
40 vertex figures
- 40 of {5}*10
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s1*s0*(s2*s1)^2*s0*s1*s2)^2> of order 4
14 facets
40 vertex figures
- 40 of {5}*10
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s1*s2)^2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 4
10 facets
- 10 of {20}*40
40 vertex figures
- 40 of {5}*10
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2, (s0*s1)^3*(s2*s1)^2*s0*s1*s0*s2*s1*s2, (s0*s1)^2*(s0*s2*s1)^2*s0*(s1*s2)^2*s1> of order 8
6 facets
20 vertex figures
- 20 of {5}*10
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1*s0*(s2*s1)^2)^2, s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 8
8 facets
20 vertex figures
- 20 of {5}*10
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1*s0*(s2*s1)^2)^2> of order 8
6 facets
20 vertex figures
- 20 of {5}*10
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, (s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2, s1*s0*s2*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 8
8 facets
20 vertex figures
- 20 of {5}*10
P/N, where N=<s0*(s1*s2)^2*s1*s0*(s1*s2)^2, (s0*s2*s1)^4*s2> of order 8
6 facets
20 vertex figures
- 20 of {5}*10
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, s0*(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2, s1*s0*s2*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 8
7 facets
20 vertex figures
- 20 of {5}*10
P/N, where N=<(s1*s0)^2*s2*s1*s0*s1*s2, s0*(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2, s1*(s2*s1*s0)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 8
7 facets
20 vertex figures
- 20 of {5}*10
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*(s1*s0*s2)^2*(s1*s0)^2*(s2*s1)^2, s1*(s2*s1*s0)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 8
6 facets
20 vertex figures
- 20 of {5}*10
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,73)(18,74)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,49)(42,50)(43,51)(44,52)(45,53)(46,54)(47,55)(48,56);; s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,32)(10,31)(11,29)(12,30)(13,27)(14,28)(15,26)(16,25)(33,65)(34,66)(35,68)(36,67)(37,70)(38,69)(39,71)(40,72)(41,80)(42,79)(43,77)(44,78)(45,75)(46,76)(47,74)(48,73)(51,52)(53,54)(57,64)(58,63)(59,61)(60,62);; s2 := ( 2,10)( 3,11)( 5,16)( 6, 7)( 8,13)(14,15)(17,65)(18,74)(19,75)(20,68)(21,80)(22,71)(23,70)(24,77)(25,73)(26,66)(27,67)(28,76)(29,72)(30,79)(31,78)(32,69)(33,49)(34,58)(35,59)(36,52)(37,64)(38,55)(39,54)(40,61)(41,57)(42,50)(43,51)(44,60)(45,56)(46,63)(47,62)(48,53);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(80)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,13)( 6,14)( 7,15)( 8,16)(17,73)(18,74)(19,75)(20,76)(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,63)(40,64)(41,49)(42,50)(43,51)(44,52)(45,53)(46,54)(47,55)(48,56); s1 := Sym(80)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,22)( 6,21)( 7,23)( 8,24)( 9,32)(10,31)(11,29)(12,30)(13,27)(14,28)(15,26)(16,25)(33,65)(34,66)(35,68)(36,67)(37,70)(38,69)(39,71)(40,72)(41,80)(42,79)(43,77)(44,78)(45,75)(46,76)(47,74)(48,73)(51,52)(53,54)(57,64)(58,63)(59,61)(60,62); s2 := Sym(80)!( 2,10)( 3,11)( 5,16)( 6, 7)( 8,13)(14,15)(17,65)(18,74)(19,75)(20,68)(21,80)(22,71)(23,70)(24,77)(25,73)(26,66)(27,67)(28,76)(29,72)(30,79)(31,78)(32,69)(33,49)(34,58)(35,59)(36,52)(37,64)(38,55)(39,54)(40,61)(41,57)(42,50)(43,51)(44,60)(45,56)(46,63)(47,62)(48,53); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.