Polytope of Type {2,6,4,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,4,8}*768a
if this polytope has a name.
Group : SmallGroup(768,1035859)
Rank : 5
Schlafli Type : {2,6,4,8}
Number of vertices, edges, etc : 2, 6, 12, 16, 8
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 : {2,6,4,4}*384, {2,6,2,8}*384
3-fold quotients : {2,2,4,8}*256a
4-fold quotients : {2,3,2,8}*192, {2,6,2,4}*192, {2,6,4,2}*192a
6-fold quotients : {2,2,4,4}*128, {2,2,2,8}*128
8-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
12-fold quotients : {2,2,2,4}*64, {2,2,4,2}*64
16-fold quotients : {2,3,2,2}*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, 27)( 4, 29)( 5, 28)( 6, 30)( 7, 32)( 8, 31)( 9, 33)( 10, 35)
( 11, 34)( 12, 36)( 13, 38)( 14, 37)( 15, 39)( 16, 41)( 17, 40)( 18, 42)
( 19, 44)( 20, 43)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 50)( 26, 49)
( 51, 75)( 52, 77)( 53, 76)( 54, 78)( 55, 80)( 56, 79)( 57, 81)( 58, 83)
( 59, 82)( 60, 84)( 61, 86)( 62, 85)( 63, 87)( 64, 89)( 65, 88)( 66, 90)
( 67, 92)( 68, 91)( 69, 93)( 70, 95)( 71, 94)( 72, 96)( 73, 98)( 74, 97)
( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)(106,131)
(107,130)(108,132)(109,134)(110,133)(111,135)(112,137)(113,136)(114,138)
(115,140)(116,139)(117,141)(118,143)(119,142)(120,144)(121,146)(122,145)
(147,171)(148,173)(149,172)(150,174)(151,176)(152,175)(153,177)(154,179)
(155,178)(156,180)(157,182)(158,181)(159,183)(160,185)(161,184)(162,186)
(163,188)(164,187)(165,189)(166,191)(167,190)(168,192)(169,194)(170,193);;
s2 := ( 3, 76)( 4, 75)( 5, 77)( 6, 79)( 7, 78)( 8, 80)( 9, 82)( 10, 81)
( 11, 83)( 12, 85)( 13, 84)( 14, 86)( 15, 88)( 16, 87)( 17, 89)( 18, 91)
( 19, 90)( 20, 92)( 21, 94)( 22, 93)( 23, 95)( 24, 97)( 25, 96)( 26, 98)
( 27, 52)( 28, 51)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 58)( 34, 57)
( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 64)( 40, 63)( 41, 65)( 42, 67)
( 43, 66)( 44, 68)( 45, 70)( 46, 69)( 47, 71)( 48, 73)( 49, 72)( 50, 74)
( 99,172)(100,171)(101,173)(102,175)(103,174)(104,176)(105,178)(106,177)
(107,179)(108,181)(109,180)(110,182)(111,184)(112,183)(113,185)(114,187)
(115,186)(116,188)(117,190)(118,189)(119,191)(120,193)(121,192)(122,194)
(123,148)(124,147)(125,149)(126,151)(127,150)(128,152)(129,154)(130,153)
(131,155)(132,157)(133,156)(134,158)(135,160)(136,159)(137,161)(138,163)
(139,162)(140,164)(141,166)(142,165)(143,167)(144,169)(145,168)(146,170);;
s3 := ( 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)(147,165)(148,166)(149,167)(150,168)
(151,169)(152,170)(153,159)(154,160)(155,161)(156,162)(157,163)(158,164)
(171,189)(172,190)(173,191)(174,192)(175,193)(176,194)(177,183)(178,184)
(179,185)(180,186)(181,187)(182,188);;
s4 := ( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,105)( 10,106)
( 11,107)( 12,108)( 13,109)( 14,110)( 15,114)( 16,115)( 17,116)( 18,111)
( 19,112)( 20,113)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)( 26,119)
( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)( 33,129)( 34,130)
( 35,131)( 36,132)( 37,133)( 38,134)( 39,138)( 40,139)( 41,140)( 42,135)
( 43,136)( 44,137)( 45,144)( 46,145)( 47,146)( 48,141)( 49,142)( 50,143)
( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)( 58,154)
( 59,155)( 60,156)( 61,157)( 62,158)( 63,162)( 64,163)( 65,164)( 66,159)
( 67,160)( 68,161)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)( 74,167)
( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)( 81,177)( 82,178)
( 83,179)( 84,180)( 85,181)( 86,182)( 87,186)( 88,187)( 89,188)( 90,183)
( 91,184)( 92,185)( 93,192)( 94,193)( 95,194)( 96,189)( 97,190)( 98,191);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*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, 27)( 4, 29)( 5, 28)( 6, 30)( 7, 32)( 8, 31)( 9, 33)
( 10, 35)( 11, 34)( 12, 36)( 13, 38)( 14, 37)( 15, 39)( 16, 41)( 17, 40)
( 18, 42)( 19, 44)( 20, 43)( 21, 45)( 22, 47)( 23, 46)( 24, 48)( 25, 50)
( 26, 49)( 51, 75)( 52, 77)( 53, 76)( 54, 78)( 55, 80)( 56, 79)( 57, 81)
( 58, 83)( 59, 82)( 60, 84)( 61, 86)( 62, 85)( 63, 87)( 64, 89)( 65, 88)
( 66, 90)( 67, 92)( 68, 91)( 69, 93)( 70, 95)( 71, 94)( 72, 96)( 73, 98)
( 74, 97)( 99,123)(100,125)(101,124)(102,126)(103,128)(104,127)(105,129)
(106,131)(107,130)(108,132)(109,134)(110,133)(111,135)(112,137)(113,136)
(114,138)(115,140)(116,139)(117,141)(118,143)(119,142)(120,144)(121,146)
(122,145)(147,171)(148,173)(149,172)(150,174)(151,176)(152,175)(153,177)
(154,179)(155,178)(156,180)(157,182)(158,181)(159,183)(160,185)(161,184)
(162,186)(163,188)(164,187)(165,189)(166,191)(167,190)(168,192)(169,194)
(170,193);
s2 := Sym(194)!( 3, 76)( 4, 75)( 5, 77)( 6, 79)( 7, 78)( 8, 80)( 9, 82)
( 10, 81)( 11, 83)( 12, 85)( 13, 84)( 14, 86)( 15, 88)( 16, 87)( 17, 89)
( 18, 91)( 19, 90)( 20, 92)( 21, 94)( 22, 93)( 23, 95)( 24, 97)( 25, 96)
( 26, 98)( 27, 52)( 28, 51)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 58)
( 34, 57)( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 64)( 40, 63)( 41, 65)
( 42, 67)( 43, 66)( 44, 68)( 45, 70)( 46, 69)( 47, 71)( 48, 73)( 49, 72)
( 50, 74)( 99,172)(100,171)(101,173)(102,175)(103,174)(104,176)(105,178)
(106,177)(107,179)(108,181)(109,180)(110,182)(111,184)(112,183)(113,185)
(114,187)(115,186)(116,188)(117,190)(118,189)(119,191)(120,193)(121,192)
(122,194)(123,148)(124,147)(125,149)(126,151)(127,150)(128,152)(129,154)
(130,153)(131,155)(132,157)(133,156)(134,158)(135,160)(136,159)(137,161)
(138,163)(139,162)(140,164)(141,166)(142,165)(143,167)(144,169)(145,168)
(146,170);
s3 := 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)(147,165)(148,166)(149,167)
(150,168)(151,169)(152,170)(153,159)(154,160)(155,161)(156,162)(157,163)
(158,164)(171,189)(172,190)(173,191)(174,192)(175,193)(176,194)(177,183)
(178,184)(179,185)(180,186)(181,187)(182,188);
s4 := Sym(194)!( 3, 99)( 4,100)( 5,101)( 6,102)( 7,103)( 8,104)( 9,105)
( 10,106)( 11,107)( 12,108)( 13,109)( 14,110)( 15,114)( 16,115)( 17,116)
( 18,111)( 19,112)( 20,113)( 21,120)( 22,121)( 23,122)( 24,117)( 25,118)
( 26,119)( 27,123)( 28,124)( 29,125)( 30,126)( 31,127)( 32,128)( 33,129)
( 34,130)( 35,131)( 36,132)( 37,133)( 38,134)( 39,138)( 40,139)( 41,140)
( 42,135)( 43,136)( 44,137)( 45,144)( 46,145)( 47,146)( 48,141)( 49,142)
( 50,143)( 51,147)( 52,148)( 53,149)( 54,150)( 55,151)( 56,152)( 57,153)
( 58,154)( 59,155)( 60,156)( 61,157)( 62,158)( 63,162)( 64,163)( 65,164)
( 66,159)( 67,160)( 68,161)( 69,168)( 70,169)( 71,170)( 72,165)( 73,166)
( 74,167)( 75,171)( 76,172)( 77,173)( 78,174)( 79,175)( 80,176)( 81,177)
( 82,178)( 83,179)( 84,180)( 85,181)( 86,182)( 87,186)( 88,187)( 89,188)
( 90,183)( 91,184)( 92,185)( 93,192)( 94,193)( 95,194)( 96,189)( 97,190)
( 98,191);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope