Overview
- Group
- SmallGroup(1296,3528)
- Rank
- 4
- Schläfli Type
- {4,6,3}
- Vertices, edges, …
- 36, 108, 81, 3
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
9-fold
18-fold
27-fold
54-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)^2> of order 2
3 facets
- 3 of 2-fold non-regular quotient of {4,6}*432b
18 vertex figures
- 18 of {6,3}*36
P/N, where N=<s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 3
3 facets
- 3 of 3-fold non-regular quotient of {4,6}*432b
12 vertex figures
- 12 of {6,3}*36
P/N, where N=<(s1*s0*s1*s2)^2> of order 3
3 facets
- 3 of 3-fold non-regular quotient of {4,6}*432b
12 vertex figures
- 12 of {6,3}*36
P/N, where N=<(s0*s1)^2*(s2*s1)^2*(s0*s2*s1)^2> of order 3
3 facets
- 3 of 3-fold non-regular quotient of {4,6}*432b
12 vertex figures
- 12 of {6,3}*36
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 3
3 facets
- 3 of 3-fold non-regular quotient of {4,6}*432b
18 vertex figures
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*s1*s2*s1*s0*s2> of order 6
3 facets
- 3 of 6-fold non-regular quotient of {4,6}*432b
6 vertex figures
- 6 of {6,3}*36
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2> of order 6
3 facets
- 3 of 6-fold non-regular quotient of {4,6}*432b
6 vertex figures
- 6 of {6,3}*36
P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 9
3 facets
- 3 of 9-fold non-regular quotient of {4,6}*432b
6 vertex figures
P/N, where N=<(s1*s2)^2, (s1*s0*s1*s2)^2> of order 9
3 facets
- 3 of 9-fold non-regular quotient of {4,6}*432b
8 vertex figures
Representations
Permutation Representation (GAP)
s0 := (28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81);; s1 := ( 4, 7)( 5, 8)( 6, 9)(10,28)(11,29)(12,30)(13,34)(14,35)(15,36)(16,31)(17,32)(18,33)(19,55)(20,56)(21,57)(22,61)(23,62)(24,63)(25,58)(26,59)(27,60)(40,43)(41,44)(42,45)(46,64)(47,65)(48,66)(49,70)(50,71)(51,72)(52,67)(53,68)(54,69)(76,79)(77,80)(78,81);; s2 := ( 1,13)( 2,15)( 3,14)( 4,10)( 5,12)( 6,11)( 7,16)( 8,18)( 9,17)(19,22)(20,24)(21,23)(26,27)(28,67)(29,69)(30,68)(31,64)(32,66)(33,65)(34,70)(35,72)(36,71)(37,58)(38,60)(39,59)(40,55)(41,57)(42,56)(43,61)(44,63)(45,62)(46,76)(47,78)(48,77)(49,73)(50,75)(51,74)(52,79)(53,81)(54,80);; s3 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,20)(11,19)(12,21)(13,26)(14,25)(15,27)(16,23)(17,22)(18,24)(28,56)(29,55)(30,57)(31,62)(32,61)(33,63)(34,59)(35,58)(36,60)(37,74)(38,73)(39,75)(40,80)(41,79)(42,81)(43,77)(44,76)(45,78)(46,65)(47,64)(48,66)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69);; 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*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2,
s0*s1*s2*s3*s1*s0*s1*s2*s1*s0*s1*s2*s3*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(81)!(28,55)(29,56)(30,57)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81); s1 := Sym(81)!( 4, 7)( 5, 8)( 6, 9)(10,28)(11,29)(12,30)(13,34)(14,35)(15,36)(16,31)(17,32)(18,33)(19,55)(20,56)(21,57)(22,61)(23,62)(24,63)(25,58)(26,59)(27,60)(40,43)(41,44)(42,45)(46,64)(47,65)(48,66)(49,70)(50,71)(51,72)(52,67)(53,68)(54,69)(76,79)(77,80)(78,81); s2 := Sym(81)!( 1,13)( 2,15)( 3,14)( 4,10)( 5,12)( 6,11)( 7,16)( 8,18)( 9,17)(19,22)(20,24)(21,23)(26,27)(28,67)(29,69)(30,68)(31,64)(32,66)(33,65)(34,70)(35,72)(36,71)(37,58)(38,60)(39,59)(40,55)(41,57)(42,56)(43,61)(44,63)(45,62)(46,76)(47,78)(48,77)(49,73)(50,75)(51,74)(52,79)(53,81)(54,80); s3 := Sym(81)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,20)(11,19)(12,21)(13,26)(14,25)(15,27)(16,23)(17,22)(18,24)(28,56)(29,55)(30,57)(31,62)(32,61)(33,63)(34,59)(35,58)(36,60)(37,74)(38,73)(39,75)(40,80)(41,79)(42,81)(43,77)(44,76)(45,78)(46,65)(47,64)(48,66)(49,71)(50,70)(51,72)(52,68)(53,67)(54,69); poly := sub<Sym(81)|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*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s0*s1*s2*s3*s1*s0*s1*s2*s1*s0*s1*s2*s3*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.