Polytope of Type {2,12,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,16}*768b
if this polytope has a name.
Group : SmallGroup(768,323453)
Rank : 4
Schlafli Type : {2,12,16}
Number of vertices, edges, etc : 2, 12, 96, 16
Order of s0s1s2s3 : 48
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 : {2,12,8}*384a
3-fold quotients : {2,4,16}*256b
4-fold quotients : {2,12,4}*192a, {2,6,8}*192
6-fold quotients : {2,4,8}*128a
8-fold quotients : {2,12,2}*96, {2,6,4}*96a
12-fold quotients : {2,4,4}*64, {2,2,8}*64
16-fold quotients : {2,6,2}*48
24-fold quotients : {2,2,4}*32, {2,4,2}*32
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, 53)( 5, 52)( 6, 54)( 7, 56)( 8, 55)( 9, 57)( 10, 59)
( 11, 58)( 12, 60)( 13, 62)( 14, 61)( 15, 63)( 16, 65)( 17, 64)( 18, 66)
( 19, 68)( 20, 67)( 21, 69)( 22, 71)( 23, 70)( 24, 72)( 25, 74)( 26, 73)
( 27, 78)( 28, 80)( 29, 79)( 30, 75)( 31, 77)( 32, 76)( 33, 84)( 34, 86)
( 35, 85)( 36, 81)( 37, 83)( 38, 82)( 39, 90)( 40, 92)( 41, 91)( 42, 87)
( 43, 89)( 44, 88)( 45, 96)( 46, 98)( 47, 97)( 48, 93)( 49, 95)( 50, 94)
( 99,147)(100,149)(101,148)(102,150)(103,152)(104,151)(105,153)(106,155)
(107,154)(108,156)(109,158)(110,157)(111,159)(112,161)(113,160)(114,162)
(115,164)(116,163)(117,165)(118,167)(119,166)(120,168)(121,170)(122,169)
(123,174)(124,176)(125,175)(126,171)(127,173)(128,172)(129,180)(130,182)
(131,181)(132,177)(133,179)(134,178)(135,186)(136,188)(137,187)(138,183)
(139,185)(140,184)(141,192)(142,194)(143,193)(144,189)(145,191)(146,190);;
s2 := ( 3, 4)( 6, 7)( 9, 13)( 10, 12)( 11, 14)( 15, 16)( 18, 19)( 21, 25)
( 22, 24)( 23, 26)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)( 32, 38)
( 39, 46)( 40, 45)( 41, 47)( 42, 49)( 43, 48)( 44, 50)( 51, 64)( 52, 63)
( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 73)( 58, 72)( 59, 74)( 60, 70)
( 61, 69)( 62, 71)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)( 80, 98)
( 81, 88)( 82, 87)( 83, 89)( 84, 91)( 85, 90)( 86, 92)( 99,124)(100,123)
(101,125)(102,127)(103,126)(104,128)(105,133)(106,132)(107,134)(108,130)
(109,129)(110,131)(111,136)(112,135)(113,137)(114,139)(115,138)(116,140)
(117,145)(118,144)(119,146)(120,142)(121,141)(122,143)(147,187)(148,186)
(149,188)(150,184)(151,183)(152,185)(153,190)(154,189)(155,191)(156,193)
(157,192)(158,194)(159,175)(160,174)(161,176)(162,172)(163,171)(164,173)
(165,178)(166,177)(167,179)(168,181)(169,180)(170,182);;
s3 := ( 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)
( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)( 34,124)
( 35,125)( 36,126)( 37,127)( 38,128)( 39,144)( 40,145)( 41,146)( 42,141)
( 43,142)( 44,143)( 45,138)( 46,139)( 47,140)( 48,135)( 49,136)( 50,137)
( 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)
( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)( 82,172)
( 83,173)( 84,174)( 85,175)( 86,176)( 87,192)( 88,193)( 89,194)( 90,189)
( 91,190)( 92,191)( 93,186)( 94,187)( 95,188)( 96,183)( 97,184)( 98,185);;
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*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*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(194)!(1,2);
s1 := Sym(194)!( 3, 51)( 4, 53)( 5, 52)( 6, 54)( 7, 56)( 8, 55)( 9, 57)
( 10, 59)( 11, 58)( 12, 60)( 13, 62)( 14, 61)( 15, 63)( 16, 65)( 17, 64)
( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 71)( 23, 70)( 24, 72)( 25, 74)
( 26, 73)( 27, 78)( 28, 80)( 29, 79)( 30, 75)( 31, 77)( 32, 76)( 33, 84)
( 34, 86)( 35, 85)( 36, 81)( 37, 83)( 38, 82)( 39, 90)( 40, 92)( 41, 91)
( 42, 87)( 43, 89)( 44, 88)( 45, 96)( 46, 98)( 47, 97)( 48, 93)( 49, 95)
( 50, 94)( 99,147)(100,149)(101,148)(102,150)(103,152)(104,151)(105,153)
(106,155)(107,154)(108,156)(109,158)(110,157)(111,159)(112,161)(113,160)
(114,162)(115,164)(116,163)(117,165)(118,167)(119,166)(120,168)(121,170)
(122,169)(123,174)(124,176)(125,175)(126,171)(127,173)(128,172)(129,180)
(130,182)(131,181)(132,177)(133,179)(134,178)(135,186)(136,188)(137,187)
(138,183)(139,185)(140,184)(141,192)(142,194)(143,193)(144,189)(145,191)
(146,190);
s2 := Sym(194)!( 3, 4)( 6, 7)( 9, 13)( 10, 12)( 11, 14)( 15, 16)( 18, 19)
( 21, 25)( 22, 24)( 23, 26)( 27, 34)( 28, 33)( 29, 35)( 30, 37)( 31, 36)
( 32, 38)( 39, 46)( 40, 45)( 41, 47)( 42, 49)( 43, 48)( 44, 50)( 51, 64)
( 52, 63)( 53, 65)( 54, 67)( 55, 66)( 56, 68)( 57, 73)( 58, 72)( 59, 74)
( 60, 70)( 61, 69)( 62, 71)( 75, 94)( 76, 93)( 77, 95)( 78, 97)( 79, 96)
( 80, 98)( 81, 88)( 82, 87)( 83, 89)( 84, 91)( 85, 90)( 86, 92)( 99,124)
(100,123)(101,125)(102,127)(103,126)(104,128)(105,133)(106,132)(107,134)
(108,130)(109,129)(110,131)(111,136)(112,135)(113,137)(114,139)(115,138)
(116,140)(117,145)(118,144)(119,146)(120,142)(121,141)(122,143)(147,187)
(148,186)(149,188)(150,184)(151,183)(152,185)(153,190)(154,189)(155,191)
(156,193)(157,192)(158,194)(159,175)(160,174)(161,176)(162,172)(163,171)
(164,173)(165,178)(166,177)(167,179)(168,181)(169,180)(170,182);
s3 := 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)( 27,129)( 28,130)( 29,131)( 30,132)( 31,133)( 32,134)( 33,123)
( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,144)( 40,145)( 41,146)
( 42,141)( 43,142)( 44,143)( 45,138)( 46,139)( 47,140)( 48,135)( 49,136)
( 50,137)( 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)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)( 81,171)
( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,192)( 88,193)( 89,194)
( 90,189)( 91,190)( 92,191)( 93,186)( 94,187)( 95,188)( 96,183)( 97,184)
( 98,185);
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*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*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 >;
to this polytope