Overview
- Group
- SmallGroup(768,1088763)
- Rank
- 4
- Schläfli Type
- {6,4,4}
- Vertices, edges, …
- 24, 48, 32, 4
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
12-fold
16-fold
24-fold
32-fold
48-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*s1)^2> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {6,4}*192b
12 vertex figures
- 12 of {4,4}*32
P/N, where N=<(s0*s1)^3> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {6,4}*192b
12 vertex figures
- 12 of {4,4}*32
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {6,4}*192b
16 vertex figures
P/N, where N=<(s0*s1)^2> of order 3
4 facets
- 4 of 3-fold non-regular quotient of {6,4}*192b
8 vertex figures
- 8 of {4,4}*32
P/N, where N=<(s1*s2)^2, s0*s1*s2*s1*s0*s2> of order 4
4 facets
- 4 of 4-fold non-regular quotient of {6,4}*192b
10 vertex figures
P/N, where N=<(s0*s1)^3, s0*(s1*s0*s2)^2*s1> of order 4
4 facets
- 4 of 4-fold non-regular quotient of {6,4}*192b
8 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s1*s2> of order 4
4 facets
- 4 of 4-fold non-regular quotient of {6,4}*192b
6 vertex figures
- 6 of {4,4}*32
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,21)(18,22)(19,24)(20,23)(27,28)(29,33)(30,34)(31,36)(32,35)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(53,57)(54,58)(55,60)(56,59)(63,64)(65,69)(66,70)(67,72)(68,71)(75,76)(77,81)(78,82)(79,84)(80,83)(87,88)(89,93)(90,94)(91,96)(92,95);; s1 := ( 1, 9)( 2,11)( 3,10)( 4,12)( 6, 7)(13,21)(14,23)(15,22)(16,24)(18,19)(25,33)(26,35)(27,34)(28,36)(30,31)(37,45)(38,47)(39,46)(40,48)(42,43)(49,69)(50,71)(51,70)(52,72)(53,65)(54,67)(55,66)(56,68)(57,61)(58,63)(59,62)(60,64)(73,93)(74,95)(75,94)(76,96)(77,89)(78,91)(79,90)(80,92)(81,85)(82,87)(83,86)(84,88);; s2 := ( 1,50)( 2,49)( 3,52)( 4,51)( 5,54)( 6,53)( 7,56)( 8,55)( 9,58)(10,57)(11,60)(12,59)(13,62)(14,61)(15,64)(16,63)(17,66)(18,65)(19,68)(20,67)(21,70)(22,69)(23,72)(24,71)(25,74)(26,73)(27,76)(28,75)(29,78)(30,77)(31,80)(32,79)(33,82)(34,81)(35,84)(36,83)(37,86)(38,85)(39,88)(40,87)(41,90)(42,89)(43,92)(44,91)(45,94)(46,93)(47,96)(48,95);; s3 := (49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96);; 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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(96)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,21)(18,22)(19,24)(20,23)(27,28)(29,33)(30,34)(31,36)(32,35)(39,40)(41,45)(42,46)(43,48)(44,47)(51,52)(53,57)(54,58)(55,60)(56,59)(63,64)(65,69)(66,70)(67,72)(68,71)(75,76)(77,81)(78,82)(79,84)(80,83)(87,88)(89,93)(90,94)(91,96)(92,95); s1 := Sym(96)!( 1, 9)( 2,11)( 3,10)( 4,12)( 6, 7)(13,21)(14,23)(15,22)(16,24)(18,19)(25,33)(26,35)(27,34)(28,36)(30,31)(37,45)(38,47)(39,46)(40,48)(42,43)(49,69)(50,71)(51,70)(52,72)(53,65)(54,67)(55,66)(56,68)(57,61)(58,63)(59,62)(60,64)(73,93)(74,95)(75,94)(76,96)(77,89)(78,91)(79,90)(80,92)(81,85)(82,87)(83,86)(84,88); s2 := Sym(96)!( 1,50)( 2,49)( 3,52)( 4,51)( 5,54)( 6,53)( 7,56)( 8,55)( 9,58)(10,57)(11,60)(12,59)(13,62)(14,61)(15,64)(16,63)(17,66)(18,65)(19,68)(20,67)(21,70)(22,69)(23,72)(24,71)(25,74)(26,73)(27,76)(28,75)(29,78)(30,77)(31,80)(32,79)(33,82)(34,81)(35,84)(36,83)(37,86)(38,85)(39,88)(40,87)(41,90)(42,89)(43,92)(44,91)(45,94)(46,93)(47,96)(48,95); s3 := Sym(96)!(49,73)(50,74)(51,75)(52,76)(53,77)(54,78)(55,79)(56,80)(57,81)(58,82)(59,83)(60,84)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,95)(72,96); 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, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.