Overview
- Group
- SmallGroup(1664,6495)
- Rank
- 3
- Schläfli Type
- {4,52}
- Vertices, edges, …
- 16, 416, 208
- Order of s0s1s2
- 104
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
13-fold
16-fold
26-fold
32-fold
52-fold
104-fold
208-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=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 2
104 facets
- 104 of {4}*8
8 vertex figures
- 8 of {52}*104
P/N, where N=<(s0*s2*s1)^3*s0*(s2*s1)^9*s2> of order 2
104 facets
- 104 of {4}*8
8 vertex figures
- 8 of {52}*104
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s1*s2> of order 4
52 facets
- 52 of {4}*8
4 vertex figures
- 4 of {52}*104
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2> of order 4
65 facets
4 vertex figures
- 4 of {52}*104
P/N, where N=<(s0*s2*s1)^3*s0*(s2*s1)^9*s2, s0*(s1*s0*s2)^2*s1*s0*(s2*s1)^11> of order 4
52 facets
- 52 of {4}*8
5 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 53, 92)( 54, 93)( 55, 94)( 56, 95)( 57, 96)( 58, 97)( 59, 98)( 60, 99)( 61,100)( 62,101)( 63,102)( 64,103)( 65,104)( 66, 79)( 67, 80)( 68, 81)( 69, 82)( 70, 83)( 71, 84)( 72, 85)( 73, 86)( 74, 87)( 75, 88)( 76, 89)( 77, 90)( 78, 91)(157,196)(158,197)(159,198)(160,199)(161,200)(162,201)(163,202)(164,203)(165,204)(166,205)(167,206)(168,207)(169,208)(170,183)(171,184)(172,185)(173,186)(174,187)(175,188)(176,189)(177,190)(178,191)(179,192)(180,193)(181,194)(182,195);; s1 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 27, 40)( 28, 52)( 29, 51)( 30, 50)( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 92)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)(105,157)(106,169)(107,168)(108,167)(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)(116,159)(117,158)(118,170)(119,182)(120,181)(121,180)(122,179)(123,178)(124,177)(125,176)(126,175)(127,174)(128,173)(129,172)(130,171)(131,196)(132,208)(133,207)(134,206)(135,205)(136,204)(137,203)(138,202)(139,201)(140,200)(141,199)(142,198)(143,197)(144,183)(145,195)(146,194)(147,193)(148,192)(149,191)(150,190)(151,189)(152,188)(153,187)(154,186)(155,185)(156,184);; s2 := ( 1,106)( 2,105)( 3,117)( 4,116)( 5,115)( 6,114)( 7,113)( 8,112)( 9,111)( 10,110)( 11,109)( 12,108)( 13,107)( 14,119)( 15,118)( 16,130)( 17,129)( 18,128)( 19,127)( 20,126)( 21,125)( 22,124)( 23,123)( 24,122)( 25,121)( 26,120)( 27,132)( 28,131)( 29,143)( 30,142)( 31,141)( 32,140)( 33,139)( 34,138)( 35,137)( 36,136)( 37,135)( 38,134)( 39,133)( 40,145)( 41,144)( 42,156)( 43,155)( 44,154)( 45,153)( 46,152)( 47,151)( 48,150)( 49,149)( 50,148)( 51,147)( 52,146)( 53,158)( 54,157)( 55,169)( 56,168)( 57,167)( 58,166)( 59,165)( 60,164)( 61,163)( 62,162)( 63,161)( 64,160)( 65,159)( 66,171)( 67,170)( 68,182)( 69,181)( 70,180)( 71,179)( 72,178)( 73,177)( 74,176)( 75,175)( 76,174)( 77,173)( 78,172)( 79,184)( 80,183)( 81,195)( 82,194)( 83,193)( 84,192)( 85,191)( 86,190)( 87,189)( 88,188)( 89,187)( 90,186)( 91,185)( 92,197)( 93,196)( 94,208)( 95,207)( 96,206)( 97,205)( 98,204)( 99,203)(100,202)(101,201)(102,200)(103,199)(104,198);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(208)!( 53, 92)( 54, 93)( 55, 94)( 56, 95)( 57, 96)( 58, 97)( 59, 98)( 60, 99)( 61,100)( 62,101)( 63,102)( 64,103)( 65,104)( 66, 79)( 67, 80)( 68, 81)( 69, 82)( 70, 83)( 71, 84)( 72, 85)( 73, 86)( 74, 87)( 75, 88)( 76, 89)( 77, 90)( 78, 91)(157,196)(158,197)(159,198)(160,199)(161,200)(162,201)(163,202)(164,203)(165,204)(166,205)(167,206)(168,207)(169,208)(170,183)(171,184)(172,185)(173,186)(174,187)(175,188)(176,189)(177,190)(178,191)(179,192)(180,193)(181,194)(182,195); s1 := Sym(208)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 27, 40)( 28, 52)( 29, 51)( 30, 50)( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 92)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)( 91, 93)(105,157)(106,169)(107,168)(108,167)(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)(116,159)(117,158)(118,170)(119,182)(120,181)(121,180)(122,179)(123,178)(124,177)(125,176)(126,175)(127,174)(128,173)(129,172)(130,171)(131,196)(132,208)(133,207)(134,206)(135,205)(136,204)(137,203)(138,202)(139,201)(140,200)(141,199)(142,198)(143,197)(144,183)(145,195)(146,194)(147,193)(148,192)(149,191)(150,190)(151,189)(152,188)(153,187)(154,186)(155,185)(156,184); s2 := Sym(208)!( 1,106)( 2,105)( 3,117)( 4,116)( 5,115)( 6,114)( 7,113)( 8,112)( 9,111)( 10,110)( 11,109)( 12,108)( 13,107)( 14,119)( 15,118)( 16,130)( 17,129)( 18,128)( 19,127)( 20,126)( 21,125)( 22,124)( 23,123)( 24,122)( 25,121)( 26,120)( 27,132)( 28,131)( 29,143)( 30,142)( 31,141)( 32,140)( 33,139)( 34,138)( 35,137)( 36,136)( 37,135)( 38,134)( 39,133)( 40,145)( 41,144)( 42,156)( 43,155)( 44,154)( 45,153)( 46,152)( 47,151)( 48,150)( 49,149)( 50,148)( 51,147)( 52,146)( 53,158)( 54,157)( 55,169)( 56,168)( 57,167)( 58,166)( 59,165)( 60,164)( 61,163)( 62,162)( 63,161)( 64,160)( 65,159)( 66,171)( 67,170)( 68,182)( 69,181)( 70,180)( 71,179)( 72,178)( 73,177)( 74,176)( 75,175)( 76,174)( 77,173)( 78,172)( 79,184)( 80,183)( 81,195)( 82,194)( 83,193)( 84,192)( 85,191)( 86,190)( 87,189)( 88,188)( 89,187)( 90,186)( 91,185)( 92,197)( 93,196)( 94,208)( 95,207)( 96,206)( 97,205)( 98,204)( 99,203)(100,202)(101,201)(102,200)(103,199)(104,198); poly := sub<Sym(208)|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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.