Overview
- Group
- SmallGroup(576,6980)
- Rank
- 4
- Schläfli Type
- {24,6,2}
- Vertices, edges, …
- 24, 72, 6, 2
- Order of s0s1s2s3
- 24
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
18-fold
24-fold
36-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := ( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(19,28)(20,29)(21,30)(22,34)(23,35)(24,36)(25,31)(26,32)(27,33)(37,55)(38,56)(39,57)(40,61)(41,62)(42,63)(43,58)(44,59)(45,60)(46,64)(47,65)(48,66)(49,70)(50,71)(51,72)(52,67)(53,68)(54,69);; s1 := ( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,67)(20,69)(21,68)(22,64)(23,66)(24,65)(25,70)(26,72)(27,71)(28,58)(29,60)(30,59)(31,55)(32,57)(33,56)(34,61)(35,63)(36,62);; s2 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,20)(22,26)(23,25)(24,27)(28,29)(31,35)(32,34)(33,36)(37,38)(40,44)(41,43)(42,45)(46,47)(49,53)(50,52)(51,54)(55,56)(58,62)(59,61)(60,63)(64,65)(67,71)(68,70)(69,72);; s3 := (73,74);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!( 4, 7)( 5, 8)( 6, 9)(13,16)(14,17)(15,18)(19,28)(20,29)(21,30)(22,34)(23,35)(24,36)(25,31)(26,32)(27,33)(37,55)(38,56)(39,57)(40,61)(41,62)(42,63)(43,58)(44,59)(45,60)(46,64)(47,65)(48,66)(49,70)(50,71)(51,72)(52,67)(53,68)(54,69); s1 := Sym(74)!( 1,40)( 2,42)( 3,41)( 4,37)( 5,39)( 6,38)( 7,43)( 8,45)( 9,44)(10,49)(11,51)(12,50)(13,46)(14,48)(15,47)(16,52)(17,54)(18,53)(19,67)(20,69)(21,68)(22,64)(23,66)(24,65)(25,70)(26,72)(27,71)(28,58)(29,60)(30,59)(31,55)(32,57)(33,56)(34,61)(35,63)(36,62); s2 := Sym(74)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,11)(13,17)(14,16)(15,18)(19,20)(22,26)(23,25)(24,27)(28,29)(31,35)(32,34)(33,36)(37,38)(40,44)(41,43)(42,45)(46,47)(49,53)(50,52)(51,54)(55,56)(58,62)(59,61)(60,63)(64,65)(67,71)(68,70)(69,72); s3 := Sym(74)!(73,74); poly := sub<Sym(74)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;