Polytope of Type {2,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,8}*768h
if this polytope has a name.
Group : SmallGroup(768,1089263)
Rank : 4
Schlafli Type : {2,12,8}
Number of vertices, edges, etc : 2, 24, 96, 16
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 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 : {2,12,4}*384c, {2,6,8}*384b
4-fold quotients : {2,3,8}*192, {2,6,4}*192
8-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
16-fold quotients : {2,3,4}*48, {2,6,2}*48
32-fold quotients : {2,3,2}*24
48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 51)( 4, 52)( 5, 56)( 6, 55)( 7, 54)( 8, 53)( 9, 58)( 10, 57)
( 11, 67)( 12, 68)( 13, 72)( 14, 71)( 15, 70)( 16, 69)( 17, 74)( 18, 73)
( 19, 59)( 20, 60)( 21, 64)( 22, 63)( 23, 62)( 24, 61)( 25, 66)( 26, 65)
( 27, 75)( 28, 76)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 82)( 34, 81)
( 35, 91)( 36, 92)( 37, 96)( 38, 95)( 39, 94)( 40, 93)( 41, 98)( 42, 97)
( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)( 50, 89)
( 99,147)(100,148)(101,152)(102,151)(103,150)(104,149)(105,154)(106,153)
(107,163)(108,164)(109,168)(110,167)(111,166)(112,165)(113,170)(114,169)
(115,155)(116,156)(117,160)(118,159)(119,158)(120,157)(121,162)(122,161)
(123,171)(124,172)(125,176)(126,175)(127,174)(128,173)(129,178)(130,177)
(131,187)(132,188)(133,192)(134,191)(135,190)(136,189)(137,194)(138,193)
(139,179)(140,180)(141,184)(142,183)(143,182)(144,181)(145,186)(146,185);;
s2 := ( 3,155)( 4,156)( 5,158)( 6,157)( 7,161)( 8,162)( 9,159)( 10,160)
( 11,147)( 12,148)( 13,150)( 14,149)( 15,153)( 16,154)( 17,151)( 18,152)
( 19,163)( 20,164)( 21,166)( 22,165)( 23,169)( 24,170)( 25,167)( 26,168)
( 27,179)( 28,180)( 29,182)( 30,181)( 31,185)( 32,186)( 33,183)( 34,184)
( 35,171)( 36,172)( 37,174)( 38,173)( 39,177)( 40,178)( 41,175)( 42,176)
( 43,187)( 44,188)( 45,190)( 46,189)( 47,193)( 48,194)( 49,191)( 50,192)
( 51,131)( 52,132)( 53,134)( 54,133)( 55,137)( 56,138)( 57,135)( 58,136)
( 59,123)( 60,124)( 61,126)( 62,125)( 63,129)( 64,130)( 65,127)( 66,128)
( 67,139)( 68,140)( 69,142)( 70,141)( 71,145)( 72,146)( 73,143)( 74,144)
( 75,107)( 76,108)( 77,110)( 78,109)( 79,113)( 80,114)( 81,111)( 82,112)
( 83, 99)( 84,100)( 85,102)( 86,101)( 87,105)( 88,106)( 89,103)( 90,104)
( 91,115)( 92,116)( 93,118)( 94,117)( 95,121)( 96,122)( 97,119)( 98,120);;
s3 := ( 3, 57)( 4, 58)( 5, 55)( 6, 56)( 7, 54)( 8, 53)( 9, 52)( 10, 51)
( 11, 65)( 12, 66)( 13, 63)( 14, 64)( 15, 62)( 16, 61)( 17, 60)( 18, 59)
( 19, 73)( 20, 74)( 21, 71)( 22, 72)( 23, 70)( 24, 69)( 25, 68)( 26, 67)
( 27, 81)( 28, 82)( 29, 79)( 30, 80)( 31, 78)( 32, 77)( 33, 76)( 34, 75)
( 35, 89)( 36, 90)( 37, 87)( 38, 88)( 39, 86)( 40, 85)( 41, 84)( 42, 83)
( 43, 97)( 44, 98)( 45, 95)( 46, 96)( 47, 94)( 48, 93)( 49, 92)( 50, 91)
( 99,153)(100,154)(101,151)(102,152)(103,150)(104,149)(105,148)(106,147)
(107,161)(108,162)(109,159)(110,160)(111,158)(112,157)(113,156)(114,155)
(115,169)(116,170)(117,167)(118,168)(119,166)(120,165)(121,164)(122,163)
(123,177)(124,178)(125,175)(126,176)(127,174)(128,173)(129,172)(130,171)
(131,185)(132,186)(133,183)(134,184)(135,182)(136,181)(137,180)(138,179)
(139,193)(140,194)(141,191)(142,192)(143,190)(144,189)(145,188)(146,187);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(194)!(1,2);
s1 := Sym(194)!( 3, 51)( 4, 52)( 5, 56)( 6, 55)( 7, 54)( 8, 53)( 9, 58)
( 10, 57)( 11, 67)( 12, 68)( 13, 72)( 14, 71)( 15, 70)( 16, 69)( 17, 74)
( 18, 73)( 19, 59)( 20, 60)( 21, 64)( 22, 63)( 23, 62)( 24, 61)( 25, 66)
( 26, 65)( 27, 75)( 28, 76)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 82)
( 34, 81)( 35, 91)( 36, 92)( 37, 96)( 38, 95)( 39, 94)( 40, 93)( 41, 98)
( 42, 97)( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)
( 50, 89)( 99,147)(100,148)(101,152)(102,151)(103,150)(104,149)(105,154)
(106,153)(107,163)(108,164)(109,168)(110,167)(111,166)(112,165)(113,170)
(114,169)(115,155)(116,156)(117,160)(118,159)(119,158)(120,157)(121,162)
(122,161)(123,171)(124,172)(125,176)(126,175)(127,174)(128,173)(129,178)
(130,177)(131,187)(132,188)(133,192)(134,191)(135,190)(136,189)(137,194)
(138,193)(139,179)(140,180)(141,184)(142,183)(143,182)(144,181)(145,186)
(146,185);
s2 := Sym(194)!( 3,155)( 4,156)( 5,158)( 6,157)( 7,161)( 8,162)( 9,159)
( 10,160)( 11,147)( 12,148)( 13,150)( 14,149)( 15,153)( 16,154)( 17,151)
( 18,152)( 19,163)( 20,164)( 21,166)( 22,165)( 23,169)( 24,170)( 25,167)
( 26,168)( 27,179)( 28,180)( 29,182)( 30,181)( 31,185)( 32,186)( 33,183)
( 34,184)( 35,171)( 36,172)( 37,174)( 38,173)( 39,177)( 40,178)( 41,175)
( 42,176)( 43,187)( 44,188)( 45,190)( 46,189)( 47,193)( 48,194)( 49,191)
( 50,192)( 51,131)( 52,132)( 53,134)( 54,133)( 55,137)( 56,138)( 57,135)
( 58,136)( 59,123)( 60,124)( 61,126)( 62,125)( 63,129)( 64,130)( 65,127)
( 66,128)( 67,139)( 68,140)( 69,142)( 70,141)( 71,145)( 72,146)( 73,143)
( 74,144)( 75,107)( 76,108)( 77,110)( 78,109)( 79,113)( 80,114)( 81,111)
( 82,112)( 83, 99)( 84,100)( 85,102)( 86,101)( 87,105)( 88,106)( 89,103)
( 90,104)( 91,115)( 92,116)( 93,118)( 94,117)( 95,121)( 96,122)( 97,119)
( 98,120);
s3 := Sym(194)!( 3, 57)( 4, 58)( 5, 55)( 6, 56)( 7, 54)( 8, 53)( 9, 52)
( 10, 51)( 11, 65)( 12, 66)( 13, 63)( 14, 64)( 15, 62)( 16, 61)( 17, 60)
( 18, 59)( 19, 73)( 20, 74)( 21, 71)( 22, 72)( 23, 70)( 24, 69)( 25, 68)
( 26, 67)( 27, 81)( 28, 82)( 29, 79)( 30, 80)( 31, 78)( 32, 77)( 33, 76)
( 34, 75)( 35, 89)( 36, 90)( 37, 87)( 38, 88)( 39, 86)( 40, 85)( 41, 84)
( 42, 83)( 43, 97)( 44, 98)( 45, 95)( 46, 96)( 47, 94)( 48, 93)( 49, 92)
( 50, 91)( 99,153)(100,154)(101,151)(102,152)(103,150)(104,149)(105,148)
(106,147)(107,161)(108,162)(109,159)(110,160)(111,158)(112,157)(113,156)
(114,155)(115,169)(116,170)(117,167)(118,168)(119,166)(120,165)(121,164)
(122,163)(123,177)(124,178)(125,175)(126,176)(127,174)(128,173)(129,172)
(130,171)(131,185)(132,186)(133,183)(134,184)(135,182)(136,181)(137,180)
(138,179)(139,193)(140,194)(141,191)(142,192)(143,190)(144,189)(145,188)
(146,187);
poly := sub<Sym(194)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3 >;
to this polytope