Overview
- Group
- SmallGroup(1728,15957)
- Rank
- 5
- Schläfli Type
- {3,2,8,18}
- Vertices, edges, …
- 3, 3, 8, 72, 18
- Order of s0s1s2s3s4
- 72
- Order of s0s1s2s3s4s3s2s1
- 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
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := (22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74)(57,75);; s3 := ( 4,40)( 5,42)( 6,41)( 7,47)( 8,46)( 9,48)(10,44)(11,43)(12,45)(13,49)(14,51)(15,50)(16,56)(17,55)(18,57)(19,53)(20,52)(21,54)(22,67)(23,69)(24,68)(25,74)(26,73)(27,75)(28,71)(29,70)(30,72)(31,58)(32,60)(33,59)(34,65)(35,64)(36,66)(37,62)(38,61)(39,63);; s4 := ( 4, 7)( 5, 9)( 6, 8)(10,11)(13,16)(14,18)(15,17)(19,20)(22,25)(23,27)(24,26)(28,29)(31,34)(32,36)(33,35)(37,38)(40,43)(41,45)(42,44)(46,47)(49,52)(50,54)(51,53)(55,56)(58,61)(59,63)(60,62)(64,65)(67,70)(68,72)(69,71)(73,74);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!(2,3); s1 := Sym(75)!(1,2); s2 := Sym(75)!(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38)(30,39)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(47,65)(48,66)(49,67)(50,68)(51,69)(52,70)(53,71)(54,72)(55,73)(56,74)(57,75); s3 := Sym(75)!( 4,40)( 5,42)( 6,41)( 7,47)( 8,46)( 9,48)(10,44)(11,43)(12,45)(13,49)(14,51)(15,50)(16,56)(17,55)(18,57)(19,53)(20,52)(21,54)(22,67)(23,69)(24,68)(25,74)(26,73)(27,75)(28,71)(29,70)(30,72)(31,58)(32,60)(33,59)(34,65)(35,64)(36,66)(37,62)(38,61)(39,63); s4 := Sym(75)!( 4, 7)( 5, 9)( 6, 8)(10,11)(13,16)(14,18)(15,17)(19,20)(22,25)(23,27)(24,26)(28,29)(31,34)(32,36)(33,35)(37,38)(40,43)(41,45)(42,44)(46,47)(49,52)(50,54)(51,53)(55,56)(58,61)(59,63)(60,62)(64,65)(67,70)(68,72)(69,71)(73,74); poly := sub<Sym(75)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;