Polytope of Type {2,8,4,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,4,6}*768b
if this polytope has a name.
Group : SmallGroup(768,1036167)
Rank : 5
Schlafli Type : {2,8,4,6}
Number of vertices, edges, etc : 2, 8, 16, 12, 6
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,4,6}*384
3-fold quotients : {2,8,4,2}*256b
4-fold quotients : {2,2,4,6}*192a, {2,4,2,6}*192
6-fold quotients : {2,4,4,2}*128
8-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
12-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
16-fold quotients : {2,2,2,3}*48
24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,108)( 10,109)
( 11,110)( 12,105)( 13,106)( 14,107)( 15,114)( 16,115)( 17,116)( 18,111)
( 19,112)( 20,113)( 21,117)( 22,118)( 23,119)( 24,120)( 25,121)( 26,122)
( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)( 33,132)( 34,133)
( 35,134)( 36,129)( 37,130)( 38,131)( 39,138)( 40,139)( 41,140)( 42,135)
( 43,136)( 44,137)( 45,141)( 46,142)( 47,143)( 48,144)( 49,145)( 50,146)
( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)( 58,157)
( 59,158)( 60,153)( 61,154)( 62,155)( 63,162)( 64,163)( 65,164)( 66,159)
( 67,160)( 68,161)( 69,165)( 70,166)( 71,167)( 72,168)( 73,169)( 74,170)
( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)( 81,180)( 82,181)
( 83,182)( 84,177)( 85,178)( 86,179)( 87,186)( 88,187)( 89,188)( 90,183)
( 91,184)( 92,185)( 93,189)( 94,190)( 95,191)( 96,192)( 97,193)( 98,194);;
s2 := ( 15, 18)( 16, 19)( 17, 20)( 21, 24)( 22, 25)( 23, 26)( 39, 42)( 40, 43)
( 41, 44)( 45, 48)( 46, 49)( 47, 50)( 51, 57)( 52, 58)( 53, 59)( 54, 60)
( 55, 61)( 56, 62)( 63, 72)( 64, 73)( 65, 74)( 66, 69)( 67, 70)( 68, 71)
( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 79, 85)( 80, 86)( 87, 96)( 88, 97)
( 89, 98)( 90, 93)( 91, 94)( 92, 95)( 99,111)(100,112)(101,113)(102,114)
(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(109,121)(110,122)
(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)
(131,143)(132,144)(133,145)(134,146)(147,168)(148,169)(149,170)(150,165)
(151,166)(152,167)(153,162)(154,163)(155,164)(156,159)(157,160)(158,161)
(171,192)(172,193)(173,194)(174,189)(175,190)(176,191)(177,186)(178,187)
(179,188)(180,183)(181,184)(182,185);;
s3 := ( 3, 75)( 4, 77)( 5, 76)( 6, 78)( 7, 80)( 8, 79)( 9, 81)( 10, 83)
( 11, 82)( 12, 84)( 13, 86)( 14, 85)( 15, 90)( 16, 92)( 17, 91)( 18, 87)
( 19, 89)( 20, 88)( 21, 96)( 22, 98)( 23, 97)( 24, 93)( 25, 95)( 26, 94)
( 27, 51)( 28, 53)( 29, 52)( 30, 54)( 31, 56)( 32, 55)( 33, 57)( 34, 59)
( 35, 58)( 36, 60)( 37, 62)( 38, 61)( 39, 66)( 40, 68)( 41, 67)( 42, 63)
( 43, 65)( 44, 64)( 45, 72)( 46, 74)( 47, 73)( 48, 69)( 49, 71)( 50, 70)
( 99,171)(100,173)(101,172)(102,174)(103,176)(104,175)(105,177)(106,179)
(107,178)(108,180)(109,182)(110,181)(111,186)(112,188)(113,187)(114,183)
(115,185)(116,184)(117,192)(118,194)(119,193)(120,189)(121,191)(122,190)
(123,147)(124,149)(125,148)(126,150)(127,152)(128,151)(129,153)(130,155)
(131,154)(132,156)(133,158)(134,157)(135,162)(136,164)(137,163)(138,159)
(139,161)(140,160)(141,168)(142,170)(143,169)(144,165)(145,167)(146,166);;
s4 := ( 3, 28)( 4, 27)( 5, 29)( 6, 31)( 7, 30)( 8, 32)( 9, 34)( 10, 33)
( 11, 35)( 12, 37)( 13, 36)( 14, 38)( 15, 40)( 16, 39)( 17, 41)( 18, 43)
( 19, 42)( 20, 44)( 21, 46)( 22, 45)( 23, 47)( 24, 49)( 25, 48)( 26, 50)
( 51, 76)( 52, 75)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 82)( 58, 81)
( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63, 88)( 64, 87)( 65, 89)( 66, 91)
( 67, 90)( 68, 92)( 69, 94)( 70, 93)( 71, 95)( 72, 97)( 73, 96)( 74, 98)
( 99,124)(100,123)(101,125)(102,127)(103,126)(104,128)(105,130)(106,129)
(107,131)(108,133)(109,132)(110,134)(111,136)(112,135)(113,137)(114,139)
(115,138)(116,140)(117,142)(118,141)(119,143)(120,145)(121,144)(122,146)
(147,172)(148,171)(149,173)(150,175)(151,174)(152,176)(153,178)(154,177)
(155,179)(156,181)(157,180)(158,182)(159,184)(160,183)(161,185)(162,187)
(163,186)(164,188)(165,190)(166,189)(167,191)(168,193)(169,192)(170,194);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,108)
( 10,109)( 11,110)( 12,105)( 13,106)( 14,107)( 15,114)( 16,115)( 17,116)
( 18,111)( 19,112)( 20,113)( 21,117)( 22,118)( 23,119)( 24,120)( 25,121)
( 26,122)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)( 33,132)
( 34,133)( 35,134)( 36,129)( 37,130)( 38,131)( 39,138)( 40,139)( 41,140)
( 42,135)( 43,136)( 44,137)( 45,141)( 46,142)( 47,143)( 48,144)( 49,145)
( 50,146)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,156)
( 58,157)( 59,158)( 60,153)( 61,154)( 62,155)( 63,162)( 64,163)( 65,164)
( 66,159)( 67,160)( 68,161)( 69,165)( 70,166)( 71,167)( 72,168)( 73,169)
( 74,170)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)( 81,180)
( 82,181)( 83,182)( 84,177)( 85,178)( 86,179)( 87,186)( 88,187)( 89,188)
( 90,183)( 91,184)( 92,185)( 93,189)( 94,190)( 95,191)( 96,192)( 97,193)
( 98,194);
s2 := Sym(194)!( 15, 18)( 16, 19)( 17, 20)( 21, 24)( 22, 25)( 23, 26)( 39, 42)
( 40, 43)( 41, 44)( 45, 48)( 46, 49)( 47, 50)( 51, 57)( 52, 58)( 53, 59)
( 54, 60)( 55, 61)( 56, 62)( 63, 72)( 64, 73)( 65, 74)( 66, 69)( 67, 70)
( 68, 71)( 75, 81)( 76, 82)( 77, 83)( 78, 84)( 79, 85)( 80, 86)( 87, 96)
( 88, 97)( 89, 98)( 90, 93)( 91, 94)( 92, 95)( 99,111)(100,112)(101,113)
(102,114)(103,115)(104,116)(105,117)(106,118)(107,119)(108,120)(109,121)
(110,122)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)
(130,142)(131,143)(132,144)(133,145)(134,146)(147,168)(148,169)(149,170)
(150,165)(151,166)(152,167)(153,162)(154,163)(155,164)(156,159)(157,160)
(158,161)(171,192)(172,193)(173,194)(174,189)(175,190)(176,191)(177,186)
(178,187)(179,188)(180,183)(181,184)(182,185);
s3 := Sym(194)!( 3, 75)( 4, 77)( 5, 76)( 6, 78)( 7, 80)( 8, 79)( 9, 81)
( 10, 83)( 11, 82)( 12, 84)( 13, 86)( 14, 85)( 15, 90)( 16, 92)( 17, 91)
( 18, 87)( 19, 89)( 20, 88)( 21, 96)( 22, 98)( 23, 97)( 24, 93)( 25, 95)
( 26, 94)( 27, 51)( 28, 53)( 29, 52)( 30, 54)( 31, 56)( 32, 55)( 33, 57)
( 34, 59)( 35, 58)( 36, 60)( 37, 62)( 38, 61)( 39, 66)( 40, 68)( 41, 67)
( 42, 63)( 43, 65)( 44, 64)( 45, 72)( 46, 74)( 47, 73)( 48, 69)( 49, 71)
( 50, 70)( 99,171)(100,173)(101,172)(102,174)(103,176)(104,175)(105,177)
(106,179)(107,178)(108,180)(109,182)(110,181)(111,186)(112,188)(113,187)
(114,183)(115,185)(116,184)(117,192)(118,194)(119,193)(120,189)(121,191)
(122,190)(123,147)(124,149)(125,148)(126,150)(127,152)(128,151)(129,153)
(130,155)(131,154)(132,156)(133,158)(134,157)(135,162)(136,164)(137,163)
(138,159)(139,161)(140,160)(141,168)(142,170)(143,169)(144,165)(145,167)
(146,166);
s4 := Sym(194)!( 3, 28)( 4, 27)( 5, 29)( 6, 31)( 7, 30)( 8, 32)( 9, 34)
( 10, 33)( 11, 35)( 12, 37)( 13, 36)( 14, 38)( 15, 40)( 16, 39)( 17, 41)
( 18, 43)( 19, 42)( 20, 44)( 21, 46)( 22, 45)( 23, 47)( 24, 49)( 25, 48)
( 26, 50)( 51, 76)( 52, 75)( 53, 77)( 54, 79)( 55, 78)( 56, 80)( 57, 82)
( 58, 81)( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63, 88)( 64, 87)( 65, 89)
( 66, 91)( 67, 90)( 68, 92)( 69, 94)( 70, 93)( 71, 95)( 72, 97)( 73, 96)
( 74, 98)( 99,124)(100,123)(101,125)(102,127)(103,126)(104,128)(105,130)
(106,129)(107,131)(108,133)(109,132)(110,134)(111,136)(112,135)(113,137)
(114,139)(115,138)(116,140)(117,142)(118,141)(119,143)(120,145)(121,144)
(122,146)(147,172)(148,171)(149,173)(150,175)(151,174)(152,176)(153,178)
(154,177)(155,179)(156,181)(157,180)(158,182)(159,184)(160,183)(161,185)
(162,187)(163,186)(164,188)(165,190)(166,189)(167,191)(168,193)(169,192)
(170,194);
poly := sub<Sym(194)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope