Overview
- Group
- SmallGroup(1920,238599)
- Rank
- 3
- Schläfli Type
- {6,30}
- Vertices, edges, …
- 32, 480, 160
- Order of s0s1s2
- 40
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
4-fold
5-fold
8-fold
10-fold
20-fold
40-fold
48-fold
80-fold
96-fold
240-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*s2)^2*s1)^2> of order 2
80 facets
- 80 of {6}*12
16 vertex figures
- 16 of {30}*60
P/N, where N=<(s1*s0)^2*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 2
80 facets
- 80 of {6}*12
16 vertex figures
- 16 of {30}*60
P/N, where N=<(s0*(s1*s2)^2*s1)^2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 4
40 facets
- 40 of {6}*12
8 vertex figures
- 8 of {30}*60
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2, (s0*(s1*s2)^2*s1)^2> of order 4
40 facets
- 40 of {6}*12
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s0*(s1*s2)^2*s1)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2> of order 4
40 facets
- 40 of {6}*12
8 vertex figures
- 8 of {30}*60
P/N, where N=<(s0*(s1*s2)^2*s1)^2, (s0*s1)^2*s2*s1*(s0*(s2*s1)^2)^2> of order 4
40 facets
- 40 of {6}*12
12 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(19,20)(21,22)(25,29)(26,30)(27,32)(28,31)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47)(51,52)(53,54)(57,61)(58,62)(59,64)(60,63)(67,68)(69,70)(73,77)(74,78)(75,80)(76,79);; s1 := ( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(17,65)(18,68)(19,67)(20,66)(21,78)(22,79)(23,80)(24,77)(25,73)(26,76)(27,75)(28,74)(29,72)(30,69)(31,70)(32,71)(33,49)(34,52)(35,51)(36,50)(37,62)(38,63)(39,64)(40,61)(41,57)(42,60)(43,59)(44,58)(45,56)(46,53)(47,54)(48,55);; s2 := ( 1,23)( 2,24)( 3,22)( 4,21)( 5,20)( 6,19)( 7,17)( 8,18)( 9,25)(10,26)(11,28)(12,27)(13,29)(14,30)(15,32)(16,31)(33,71)(34,72)(35,70)(36,69)(37,68)(38,67)(39,65)(40,66)(41,73)(42,74)(43,76)(44,75)(45,77)(46,78)(47,80)(48,79)(49,55)(50,56)(51,54)(52,53)(59,60)(63,64);; 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,
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0,
s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(80)!( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(19,20)(21,22)(25,29)(26,30)(27,32)(28,31)(35,36)(37,38)(41,45)(42,46)(43,48)(44,47)(51,52)(53,54)(57,61)(58,62)(59,64)(60,63)(67,68)(69,70)(73,77)(74,78)(75,80)(76,79); s1 := Sym(80)!( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(17,65)(18,68)(19,67)(20,66)(21,78)(22,79)(23,80)(24,77)(25,73)(26,76)(27,75)(28,74)(29,72)(30,69)(31,70)(32,71)(33,49)(34,52)(35,51)(36,50)(37,62)(38,63)(39,64)(40,61)(41,57)(42,60)(43,59)(44,58)(45,56)(46,53)(47,54)(48,55); s2 := Sym(80)!( 1,23)( 2,24)( 3,22)( 4,21)( 5,20)( 6,19)( 7,17)( 8,18)( 9,25)(10,26)(11,28)(12,27)(13,29)(14,30)(15,32)(16,31)(33,71)(34,72)(35,70)(36,69)(37,68)(38,67)(39,65)(40,66)(41,73)(42,74)(43,76)(44,75)(45,77)(46,78)(47,80)(48,79)(49,55)(50,56)(51,54)(52,53)(59,60)(63,64); 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, s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0, s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 >;
References
None.
to this polytope.