Overview
- Group
- SmallGroup(1008,500)
- Rank
- 3
- Schläfli Type
- {28,18}
- Vertices, edges, …
- 28, 252, 18
- Order of s0s1s2
- 63
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
7-fold
14-fold
21-fold
42-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 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 75)( 14, 76)( 15, 73)( 16, 74)( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)( 24, 82)( 25, 63)( 26, 64)( 27, 61)( 28, 62)( 29, 67)( 30, 68)( 31, 65)( 32, 66)( 33, 71)( 34, 72)( 35, 69)( 36, 70)( 37, 51)( 38, 52)( 39, 49)( 40, 50)( 41, 55)( 42, 56)( 43, 53)( 44, 54)( 45, 59)( 46, 60)( 47, 57)( 48, 58)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97,159)( 98,160)( 99,157)(100,158)(101,163)(102,164)(103,161)(104,162)(105,167)(106,168)(107,165)(108,166)(109,147)(110,148)(111,145)(112,146)(113,151)(114,152)(115,149)(116,150)(117,155)(118,156)(119,153)(120,154)(121,135)(122,136)(123,133)(124,134)(125,139)(126,140)(127,137)(128,138)(129,143)(130,144)(131,141)(132,142)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,243)(182,244)(183,241)(184,242)(185,247)(186,248)(187,245)(188,246)(189,251)(190,252)(191,249)(192,250)(193,231)(194,232)(195,229)(196,230)(197,235)(198,236)(199,233)(200,234)(201,239)(202,240)(203,237)(204,238)(205,219)(206,220)(207,217)(208,218)(209,223)(210,224)(211,221)(212,222)(213,227)(214,228)(215,225)(216,226);; s1 := ( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 21)( 6, 22)( 7, 24)( 8, 23)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 25, 73)( 26, 74)( 27, 76)( 28, 75)( 29, 81)( 30, 82)( 31, 84)( 32, 83)( 33, 77)( 34, 78)( 35, 80)( 36, 79)( 37, 61)( 38, 62)( 39, 64)( 40, 63)( 41, 69)( 42, 70)( 43, 72)( 44, 71)( 45, 65)( 46, 66)( 47, 68)( 48, 67)( 51, 52)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,177)( 98,178)( 99,180)(100,179)(101,173)(102,174)(103,176)(104,175)(105,169)(106,170)(107,172)(108,171)(109,249)(110,250)(111,252)(112,251)(113,245)(114,246)(115,248)(116,247)(117,241)(118,242)(119,244)(120,243)(121,237)(122,238)(123,240)(124,239)(125,233)(126,234)(127,236)(128,235)(129,229)(130,230)(131,232)(132,231)(133,225)(134,226)(135,228)(136,227)(137,221)(138,222)(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,213)(146,214)(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)(154,206)(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195);; s2 := ( 1, 85)( 2, 88)( 3, 87)( 4, 86)( 5, 93)( 6, 96)( 7, 95)( 8, 94)( 9, 89)( 10, 92)( 11, 91)( 12, 90)( 13, 97)( 14,100)( 15, 99)( 16, 98)( 17,105)( 18,108)( 19,107)( 20,106)( 21,101)( 22,104)( 23,103)( 24,102)( 25,109)( 26,112)( 27,111)( 28,110)( 29,117)( 30,120)( 31,119)( 32,118)( 33,113)( 34,116)( 35,115)( 36,114)( 37,121)( 38,124)( 39,123)( 40,122)( 41,129)( 42,132)( 43,131)( 44,130)( 45,125)( 46,128)( 47,127)( 48,126)( 49,133)( 50,136)( 51,135)( 52,134)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,145)( 62,148)( 63,147)( 64,146)( 65,153)( 66,156)( 67,155)( 68,154)( 69,149)( 70,152)( 71,151)( 72,150)( 73,157)( 74,160)( 75,159)( 76,158)( 77,165)( 78,168)( 79,167)( 80,166)( 81,161)( 82,164)( 83,163)( 84,162)(169,177)(170,180)(171,179)(172,178)(174,176)(181,189)(182,192)(183,191)(184,190)(186,188)(193,201)(194,204)(195,203)(196,202)(198,200)(205,213)(206,216)(207,215)(208,214)(210,212)(217,225)(218,228)(219,227)(220,226)(222,224)(229,237)(230,240)(231,239)(232,238)(234,236)(241,249)(242,252)(243,251)(244,250)(246,248);; 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*s2*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,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(252)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 75)( 14, 76)( 15, 73)( 16, 74)( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)( 24, 82)( 25, 63)( 26, 64)( 27, 61)( 28, 62)( 29, 67)( 30, 68)( 31, 65)( 32, 66)( 33, 71)( 34, 72)( 35, 69)( 36, 70)( 37, 51)( 38, 52)( 39, 49)( 40, 50)( 41, 55)( 42, 56)( 43, 53)( 44, 54)( 45, 59)( 46, 60)( 47, 57)( 48, 58)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97,159)( 98,160)( 99,157)(100,158)(101,163)(102,164)(103,161)(104,162)(105,167)(106,168)(107,165)(108,166)(109,147)(110,148)(111,145)(112,146)(113,151)(114,152)(115,149)(116,150)(117,155)(118,156)(119,153)(120,154)(121,135)(122,136)(123,133)(124,134)(125,139)(126,140)(127,137)(128,138)(129,143)(130,144)(131,141)(132,142)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,243)(182,244)(183,241)(184,242)(185,247)(186,248)(187,245)(188,246)(189,251)(190,252)(191,249)(192,250)(193,231)(194,232)(195,229)(196,230)(197,235)(198,236)(199,233)(200,234)(201,239)(202,240)(203,237)(204,238)(205,219)(206,220)(207,217)(208,218)(209,223)(210,224)(211,221)(212,222)(213,227)(214,228)(215,225)(216,226); s1 := Sym(252)!( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 21)( 6, 22)( 7, 24)( 8, 23)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 25, 73)( 26, 74)( 27, 76)( 28, 75)( 29, 81)( 30, 82)( 31, 84)( 32, 83)( 33, 77)( 34, 78)( 35, 80)( 36, 79)( 37, 61)( 38, 62)( 39, 64)( 40, 63)( 41, 69)( 42, 70)( 43, 72)( 44, 71)( 45, 65)( 46, 66)( 47, 68)( 48, 67)( 51, 52)( 53, 57)( 54, 58)( 55, 60)( 56, 59)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,177)( 98,178)( 99,180)(100,179)(101,173)(102,174)(103,176)(104,175)(105,169)(106,170)(107,172)(108,171)(109,249)(110,250)(111,252)(112,251)(113,245)(114,246)(115,248)(116,247)(117,241)(118,242)(119,244)(120,243)(121,237)(122,238)(123,240)(124,239)(125,233)(126,234)(127,236)(128,235)(129,229)(130,230)(131,232)(132,231)(133,225)(134,226)(135,228)(136,227)(137,221)(138,222)(139,224)(140,223)(141,217)(142,218)(143,220)(144,219)(145,213)(146,214)(147,216)(148,215)(149,209)(150,210)(151,212)(152,211)(153,205)(154,206)(155,208)(156,207)(157,201)(158,202)(159,204)(160,203)(161,197)(162,198)(163,200)(164,199)(165,193)(166,194)(167,196)(168,195); s2 := Sym(252)!( 1, 85)( 2, 88)( 3, 87)( 4, 86)( 5, 93)( 6, 96)( 7, 95)( 8, 94)( 9, 89)( 10, 92)( 11, 91)( 12, 90)( 13, 97)( 14,100)( 15, 99)( 16, 98)( 17,105)( 18,108)( 19,107)( 20,106)( 21,101)( 22,104)( 23,103)( 24,102)( 25,109)( 26,112)( 27,111)( 28,110)( 29,117)( 30,120)( 31,119)( 32,118)( 33,113)( 34,116)( 35,115)( 36,114)( 37,121)( 38,124)( 39,123)( 40,122)( 41,129)( 42,132)( 43,131)( 44,130)( 45,125)( 46,128)( 47,127)( 48,126)( 49,133)( 50,136)( 51,135)( 52,134)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,145)( 62,148)( 63,147)( 64,146)( 65,153)( 66,156)( 67,155)( 68,154)( 69,149)( 70,152)( 71,151)( 72,150)( 73,157)( 74,160)( 75,159)( 76,158)( 77,165)( 78,168)( 79,167)( 80,166)( 81,161)( 82,164)( 83,163)( 84,162)(169,177)(170,180)(171,179)(172,178)(174,176)(181,189)(182,192)(183,191)(184,190)(186,188)(193,201)(194,204)(195,203)(196,202)(198,200)(205,213)(206,216)(207,215)(208,214)(210,212)(217,225)(218,228)(219,227)(220,226)(222,224)(229,237)(230,240)(231,239)(232,238)(234,236)(241,249)(242,252)(243,251)(244,250)(246,248); 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*s0*s1*s0*s1*s2*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, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.