Overview
- Group
- SmallGroup(384,17873)
- Rank
- 4
- Schläfli Type
- {4,12,4}
- Vertices, edges, …
- 4, 24, 24, 4
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
Covers minimal covers in bold
2-fold
3-fold
5-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1,27)( 2,28)( 3,25)( 4,26)( 5,31)( 6,32)( 7,29)( 8,30)( 9,35)(10,36)(11,33)(12,34)(13,39)(14,40)(15,37)(16,38)(17,43)(18,44)(19,41)(20,42)(21,47)(22,48)(23,45)(24,46)(49,75)(50,76)(51,73)(52,74)(53,79)(54,80)(55,77)(56,78)(57,83)(58,84)(59,81)(60,82)(61,87)(62,88)(63,85)(64,86)(65,91)(66,92)(67,89)(68,90)(69,95)(70,96)(71,93)(72,94);; s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)(70,91)(71,90)(72,92);; s2 := ( 1,57)( 2,60)( 3,59)( 4,58)( 5,53)( 6,56)( 7,55)( 8,54)( 9,49)(10,52)(11,51)(12,50)(13,69)(14,72)(15,71)(16,70)(17,65)(18,68)(19,67)(20,66)(21,61)(22,64)(23,63)(24,62)(25,81)(26,84)(27,83)(28,82)(29,77)(30,80)(31,79)(32,78)(33,73)(34,76)(35,75)(36,74)(37,93)(38,96)(39,95)(40,94)(41,89)(42,92)(43,91)(44,90)(45,85)(46,88)(47,87)(48,86);; s3 := (49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)(60,72)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)(84,96);; 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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(96)!( 1,27)( 2,28)( 3,25)( 4,26)( 5,31)( 6,32)( 7,29)( 8,30)( 9,35)(10,36)(11,33)(12,34)(13,39)(14,40)(15,37)(16,38)(17,43)(18,44)(19,41)(20,42)(21,47)(22,48)(23,45)(24,46)(49,75)(50,76)(51,73)(52,74)(53,79)(54,80)(55,77)(56,78)(57,83)(58,84)(59,81)(60,82)(61,87)(62,88)(63,85)(64,86)(65,91)(66,92)(67,89)(68,90)(69,95)(70,96)(71,93)(72,94); s1 := Sym(96)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(26,27)(29,33)(30,35)(31,34)(32,36)(38,39)(41,45)(42,47)(43,46)(44,48)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)(70,91)(71,90)(72,92); s2 := Sym(96)!( 1,57)( 2,60)( 3,59)( 4,58)( 5,53)( 6,56)( 7,55)( 8,54)( 9,49)(10,52)(11,51)(12,50)(13,69)(14,72)(15,71)(16,70)(17,65)(18,68)(19,67)(20,66)(21,61)(22,64)(23,63)(24,62)(25,81)(26,84)(27,83)(28,82)(29,77)(30,80)(31,79)(32,78)(33,73)(34,76)(35,75)(36,74)(37,93)(38,96)(39,95)(40,94)(41,89)(42,92)(43,91)(44,90)(45,85)(46,88)(47,87)(48,86); s3 := Sym(96)!(49,61)(50,62)(51,63)(52,64)(53,65)(54,66)(55,67)(56,68)(57,69)(58,70)(59,71)(60,72)(73,85)(74,86)(75,87)(76,88)(77,89)(78,90)(79,91)(80,92)(81,93)(82,94)(83,95)(84,96); poly := sub<Sym(96)|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, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.