Overview
- Group
- SmallGroup(128,351)
- Rank
- 3
- Schläfli Type
- {8,8}
- Vertices, edges, …
- 8, 32, 8
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 2
- Also known as
- {8,8|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
- Self-Dual
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
- {16,16}*512b
- {16,16}*512e
- {16,16}*512h
- {16,16}*512k
- {8,16}*512c
- {16,8}*512c
- {8,16}*512d
- {16,8}*512d
- {8,16}*512e
- {16,8}*512e
- {8,16}*512f
- {16,8}*512f
- {8,8}*512a
- {8,8}*512b
- {8,8}*512c
- {8,32}*512b
- {32,8}*512b
- {8,32}*512d
- {32,8}*512d
5-fold
6-fold
- {8,24}*768a
- {24,8}*768a
- {8,48}*768d
- {48,8}*768d
- {16,24}*768d
- {24,16}*768d
- {8,48}*768f
- {48,8}*768f
- {16,24}*768f
- {24,16}*768f
7-fold
9-fold
- {8,72}*1152c
- {72,8}*1152c
- {24,24}*1152b
- {24,24}*1152e
- {24,24}*1152h
- {8,8}*1152a
- {8,24}*1152c
- {24,8}*1152c
10-fold
- {8,40}*1280a
- {40,8}*1280a
- {8,80}*1280d
- {80,8}*1280d
- {16,40}*1280d
- {40,16}*1280d
- {8,80}*1280f
- {80,8}*1280f
- {16,40}*1280f
- {40,16}*1280f
11-fold
13-fold
14-fold
- {8,56}*1792a
- {56,8}*1792a
- {8,112}*1792d
- {112,8}*1792d
- {16,56}*1792d
- {56,16}*1792d
- {8,112}*1792f
- {112,8}*1792f
- {16,56}*1792f
- {56,16}*1792f
15-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,26)(10,25)(11,28)(12,27)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)(37,54)(38,53)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,61)(46,62)(47,63)(48,64);; s1 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,21)(18,22)(19,23)(20,24)(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,43)(36,44)(37,46)(38,45)(39,48)(40,47)(49,62)(50,61)(51,64)(52,63)(53,58)(54,57)(55,60)(56,59);; s2 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,60)(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,44)(26,43)(27,42)(28,41)(29,48)(30,47)(31,46)(32,45);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(64)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,22)( 6,21)( 7,24)( 8,23)( 9,26)(10,25)(11,28)(12,27)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)(37,54)(38,53)(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,61)(46,62)(47,63)(48,64); s1 := Sym(64)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,21)(18,22)(19,23)(20,24)(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,43)(36,44)(37,46)(38,45)(39,48)(40,47)(49,62)(50,61)(51,64)(52,63)(53,58)(54,57)(55,60)(56,59); s2 := Sym(64)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,60)(10,59)(11,58)(12,57)(13,64)(14,63)(15,62)(16,61)(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,44)(26,43)(27,42)(28,41)(29,48)(30,47)(31,46)(32,45); poly := sub<Sym(64)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.