Overview
- Group
- SmallGroup(1008,158)
- Rank
- 3
- Schläfli Type
- {18,28}
- Vertices, edges, …
- 18, 252, 28
- Order of s0s1s2
- 252
- Order of s0s1s2s1
- 2
- Also known as
- {18,28|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
7-fold
9-fold
14-fold
18-fold
21-fold
28-fold
36-fold
42-fold
63-fold
84-fold
126-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 22, 45)( 23, 44)( 24, 43)( 25, 48)( 26, 47)( 27, 46)( 28, 51)( 29, 50)( 30, 49)( 31, 54)( 32, 53)( 33, 52)( 34, 57)( 35, 56)( 36, 55)( 37, 60)( 38, 59)( 39, 58)( 40, 63)( 41, 62)( 42, 61)( 65, 66)( 68, 69)( 71, 72)( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 85,108)( 86,107)( 87,106)( 88,111)( 89,110)( 90,109)( 91,114)( 92,113)( 93,112)( 94,117)( 95,116)( 96,115)( 97,120)( 98,119)( 99,118)(100,123)(101,122)(102,121)(103,126)(104,125)(105,124)(128,129)(131,132)(134,135)(137,138)(140,141)(143,144)(146,147)(148,171)(149,170)(150,169)(151,174)(152,173)(153,172)(154,177)(155,176)(156,175)(157,180)(158,179)(159,178)(160,183)(161,182)(162,181)(163,186)(164,185)(165,184)(166,189)(167,188)(168,187)(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)(209,210)(211,234)(212,233)(213,232)(214,237)(215,236)(216,235)(217,240)(218,239)(219,238)(220,243)(221,242)(222,241)(223,246)(224,245)(225,244)(226,249)(227,248)(228,247)(229,252)(230,251)(231,250);; s1 := ( 1, 22)( 2, 24)( 3, 23)( 4, 40)( 5, 42)( 6, 41)( 7, 37)( 8, 39)( 9, 38)( 10, 34)( 11, 36)( 12, 35)( 13, 31)( 14, 33)( 15, 32)( 16, 28)( 17, 30)( 18, 29)( 19, 25)( 20, 27)( 21, 26)( 43, 45)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)( 64, 85)( 65, 87)( 66, 86)( 67,103)( 68,105)( 69,104)( 70,100)( 71,102)( 72,101)( 73, 97)( 74, 99)( 75, 98)( 76, 94)( 77, 96)( 78, 95)( 79, 91)( 80, 93)( 81, 92)( 82, 88)( 83, 90)( 84, 89)(106,108)(109,126)(110,125)(111,124)(112,123)(113,122)(114,121)(115,120)(116,119)(117,118)(127,211)(128,213)(129,212)(130,229)(131,231)(132,230)(133,226)(134,228)(135,227)(136,223)(137,225)(138,224)(139,220)(140,222)(141,221)(142,217)(143,219)(144,218)(145,214)(146,216)(147,215)(148,190)(149,192)(150,191)(151,208)(152,210)(153,209)(154,205)(155,207)(156,206)(157,202)(158,204)(159,203)(160,199)(161,201)(162,200)(163,196)(164,198)(165,197)(166,193)(167,195)(168,194)(169,234)(170,233)(171,232)(172,252)(173,251)(174,250)(175,249)(176,248)(177,247)(178,246)(179,245)(180,244)(181,243)(182,242)(183,241)(184,240)(185,239)(186,238)(187,237)(188,236)(189,235);; s2 := ( 1,130)( 2,131)( 3,132)( 4,127)( 5,128)( 6,129)( 7,145)( 8,146)( 9,147)( 10,142)( 11,143)( 12,144)( 13,139)( 14,140)( 15,141)( 16,136)( 17,137)( 18,138)( 19,133)( 20,134)( 21,135)( 22,151)( 23,152)( 24,153)( 25,148)( 26,149)( 27,150)( 28,166)( 29,167)( 30,168)( 31,163)( 32,164)( 33,165)( 34,160)( 35,161)( 36,162)( 37,157)( 38,158)( 39,159)( 40,154)( 41,155)( 42,156)( 43,172)( 44,173)( 45,174)( 46,169)( 47,170)( 48,171)( 49,187)( 50,188)( 51,189)( 52,184)( 53,185)( 54,186)( 55,181)( 56,182)( 57,183)( 58,178)( 59,179)( 60,180)( 61,175)( 62,176)( 63,177)( 64,193)( 65,194)( 66,195)( 67,190)( 68,191)( 69,192)( 70,208)( 71,209)( 72,210)( 73,205)( 74,206)( 75,207)( 76,202)( 77,203)( 78,204)( 79,199)( 80,200)( 81,201)( 82,196)( 83,197)( 84,198)( 85,214)( 86,215)( 87,216)( 88,211)( 89,212)( 90,213)( 91,229)( 92,230)( 93,231)( 94,226)( 95,227)( 96,228)( 97,223)( 98,224)( 99,225)(100,220)(101,221)(102,222)(103,217)(104,218)(105,219)(106,235)(107,236)(108,237)(109,232)(110,233)(111,234)(112,250)(113,251)(114,252)(115,247)(116,248)(117,249)(118,244)(119,245)(120,246)(121,241)(122,242)(123,243)(124,238)(125,239)(126,240);; 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*s0*s1*s0*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*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(252)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 22, 45)( 23, 44)( 24, 43)( 25, 48)( 26, 47)( 27, 46)( 28, 51)( 29, 50)( 30, 49)( 31, 54)( 32, 53)( 33, 52)( 34, 57)( 35, 56)( 36, 55)( 37, 60)( 38, 59)( 39, 58)( 40, 63)( 41, 62)( 42, 61)( 65, 66)( 68, 69)( 71, 72)( 74, 75)( 77, 78)( 80, 81)( 83, 84)( 85,108)( 86,107)( 87,106)( 88,111)( 89,110)( 90,109)( 91,114)( 92,113)( 93,112)( 94,117)( 95,116)( 96,115)( 97,120)( 98,119)( 99,118)(100,123)(101,122)(102,121)(103,126)(104,125)(105,124)(128,129)(131,132)(134,135)(137,138)(140,141)(143,144)(146,147)(148,171)(149,170)(150,169)(151,174)(152,173)(153,172)(154,177)(155,176)(156,175)(157,180)(158,179)(159,178)(160,183)(161,182)(162,181)(163,186)(164,185)(165,184)(166,189)(167,188)(168,187)(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)(209,210)(211,234)(212,233)(213,232)(214,237)(215,236)(216,235)(217,240)(218,239)(219,238)(220,243)(221,242)(222,241)(223,246)(224,245)(225,244)(226,249)(227,248)(228,247)(229,252)(230,251)(231,250); s1 := Sym(252)!( 1, 22)( 2, 24)( 3, 23)( 4, 40)( 5, 42)( 6, 41)( 7, 37)( 8, 39)( 9, 38)( 10, 34)( 11, 36)( 12, 35)( 13, 31)( 14, 33)( 15, 32)( 16, 28)( 17, 30)( 18, 29)( 19, 25)( 20, 27)( 21, 26)( 43, 45)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)( 64, 85)( 65, 87)( 66, 86)( 67,103)( 68,105)( 69,104)( 70,100)( 71,102)( 72,101)( 73, 97)( 74, 99)( 75, 98)( 76, 94)( 77, 96)( 78, 95)( 79, 91)( 80, 93)( 81, 92)( 82, 88)( 83, 90)( 84, 89)(106,108)(109,126)(110,125)(111,124)(112,123)(113,122)(114,121)(115,120)(116,119)(117,118)(127,211)(128,213)(129,212)(130,229)(131,231)(132,230)(133,226)(134,228)(135,227)(136,223)(137,225)(138,224)(139,220)(140,222)(141,221)(142,217)(143,219)(144,218)(145,214)(146,216)(147,215)(148,190)(149,192)(150,191)(151,208)(152,210)(153,209)(154,205)(155,207)(156,206)(157,202)(158,204)(159,203)(160,199)(161,201)(162,200)(163,196)(164,198)(165,197)(166,193)(167,195)(168,194)(169,234)(170,233)(171,232)(172,252)(173,251)(174,250)(175,249)(176,248)(177,247)(178,246)(179,245)(180,244)(181,243)(182,242)(183,241)(184,240)(185,239)(186,238)(187,237)(188,236)(189,235); s2 := Sym(252)!( 1,130)( 2,131)( 3,132)( 4,127)( 5,128)( 6,129)( 7,145)( 8,146)( 9,147)( 10,142)( 11,143)( 12,144)( 13,139)( 14,140)( 15,141)( 16,136)( 17,137)( 18,138)( 19,133)( 20,134)( 21,135)( 22,151)( 23,152)( 24,153)( 25,148)( 26,149)( 27,150)( 28,166)( 29,167)( 30,168)( 31,163)( 32,164)( 33,165)( 34,160)( 35,161)( 36,162)( 37,157)( 38,158)( 39,159)( 40,154)( 41,155)( 42,156)( 43,172)( 44,173)( 45,174)( 46,169)( 47,170)( 48,171)( 49,187)( 50,188)( 51,189)( 52,184)( 53,185)( 54,186)( 55,181)( 56,182)( 57,183)( 58,178)( 59,179)( 60,180)( 61,175)( 62,176)( 63,177)( 64,193)( 65,194)( 66,195)( 67,190)( 68,191)( 69,192)( 70,208)( 71,209)( 72,210)( 73,205)( 74,206)( 75,207)( 76,202)( 77,203)( 78,204)( 79,199)( 80,200)( 81,201)( 82,196)( 83,197)( 84,198)( 85,214)( 86,215)( 87,216)( 88,211)( 89,212)( 90,213)( 91,229)( 92,230)( 93,231)( 94,226)( 95,227)( 96,228)( 97,223)( 98,224)( 99,225)(100,220)(101,221)(102,222)(103,217)(104,218)(105,219)(106,235)(107,236)(108,237)(109,232)(110,233)(111,234)(112,250)(113,251)(114,252)(115,247)(116,248)(117,249)(118,244)(119,245)(120,246)(121,241)(122,242)(123,243)(124,238)(125,239)(126,240); poly := sub<Sym(252)|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*s0*s1*s0*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*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.