Questions?
See the FAQ
or other info.

# Polytope of Type {30,4}

Atlas Canonical Name : {30,4}*960b
if this polytope has a name.
Group : SmallGroup(960,11092)
Rank : 3
Schlafli Type : {30,4}
Number of vertices, edges, etc : 120, 240, 16
Order of s0s1s2 : 60
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{30,4,2} of size 1920
Vertex Figure Of :
{2,30,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {30,4}*480
4-fold quotients : {30,4}*240a, {15,4}*240, {30,4}*240b, {30,4}*240c
5-fold quotients : {6,4}*192b
8-fold quotients : {15,4}*120, {30,2}*120
10-fold quotients : {6,4}*96
12-fold quotients : {10,4}*80
16-fold quotients : {15,2}*60
20-fold quotients : {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
24-fold quotients : {10,2}*40
40-fold quotients : {3,4}*24, {6,2}*24
48-fold quotients : {5,2}*20
60-fold quotients : {2,4}*16
80-fold quotients : {3,2}*12
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {60,4}*1920d, {30,8}*1920f, {30,8}*1920g, {60,4}*1920e, {30,4}*1920b
Permutation Representation (GAP) :
```s0 := (  2,  3)(  5, 17)(  6, 19)(  7, 18)(  8, 20)(  9, 13)( 10, 15)( 11, 14)
( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)( 27, 58)
( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)( 35, 50)
( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)( 66, 79)
( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)( 90,115)
( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)( 98,107)
( 99,106)(100,108)(122,123)(125,137)(126,139)(127,138)(128,140)(129,133)
(130,135)(131,134)(132,136)(141,161)(142,163)(143,162)(144,164)(145,177)
(146,179)(147,178)(148,180)(149,173)(150,175)(151,174)(152,176)(153,169)
(154,171)(155,170)(156,172)(157,165)(158,167)(159,166)(160,168)(182,183)
(185,197)(186,199)(187,198)(188,200)(189,193)(190,195)(191,194)(192,196)
(201,221)(202,223)(203,222)(204,224)(205,237)(206,239)(207,238)(208,240)
(209,233)(210,235)(211,234)(212,236)(213,229)(214,231)(215,230)(216,232)
(217,225)(218,227)(219,226)(220,228);;
s1 := (  1, 25)(  2, 26)(  3, 28)(  4, 27)(  5, 21)(  6, 22)(  7, 24)(  8, 23)
(  9, 37)( 10, 38)( 11, 40)( 12, 39)( 13, 33)( 14, 34)( 15, 36)( 16, 35)
( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 41, 45)( 42, 46)( 43, 48)( 44, 47)
( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 55, 56)( 61, 85)( 62, 86)( 63, 88)
( 64, 87)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 97)( 70, 98)( 71,100)
( 72, 99)( 73, 93)( 74, 94)( 75, 96)( 76, 95)( 77, 89)( 78, 90)( 79, 92)
( 80, 91)(101,105)(102,106)(103,108)(104,107)(109,117)(110,118)(111,120)
(112,119)(115,116)(121,205)(122,206)(123,208)(124,207)(125,201)(126,202)
(127,204)(128,203)(129,217)(130,218)(131,220)(132,219)(133,213)(134,214)
(135,216)(136,215)(137,209)(138,210)(139,212)(140,211)(141,185)(142,186)
(143,188)(144,187)(145,181)(146,182)(147,184)(148,183)(149,197)(150,198)
(151,200)(152,199)(153,193)(154,194)(155,196)(156,195)(157,189)(158,190)
(159,192)(160,191)(161,225)(162,226)(163,228)(164,227)(165,221)(166,222)
(167,224)(168,223)(169,237)(170,238)(171,240)(172,239)(173,233)(174,234)
(175,236)(176,235)(177,229)(178,230)(179,232)(180,231);;
s2 := (  1,124)(  2,123)(  3,122)(  4,121)(  5,128)(  6,127)(  7,126)(  8,125)
(  9,132)( 10,131)( 11,130)( 12,129)( 13,136)( 14,135)( 15,134)( 16,133)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,144)( 22,143)( 23,142)( 24,141)
( 25,148)( 26,147)( 27,146)( 28,145)( 29,152)( 30,151)( 31,150)( 32,149)
( 33,156)( 34,155)( 35,154)( 36,153)( 37,160)( 38,159)( 39,158)( 40,157)
( 41,164)( 42,163)( 43,162)( 44,161)( 45,168)( 46,167)( 47,166)( 48,165)
( 49,172)( 50,171)( 51,170)( 52,169)( 53,176)( 54,175)( 55,174)( 56,173)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,184)( 62,183)( 63,182)( 64,181)
( 65,188)( 66,187)( 67,186)( 68,185)( 69,192)( 70,191)( 71,190)( 72,189)
( 73,196)( 74,195)( 75,194)( 76,193)( 77,200)( 78,199)( 79,198)( 80,197)
( 81,204)( 82,203)( 83,202)( 84,201)( 85,208)( 86,207)( 87,206)( 88,205)
( 89,212)( 90,211)( 91,210)( 92,209)( 93,216)( 94,215)( 95,214)( 96,213)
( 97,220)( 98,219)( 99,218)(100,217)(101,224)(102,223)(103,222)(104,221)
(105,228)(106,227)(107,226)(108,225)(109,232)(110,231)(111,230)(112,229)
(113,236)(114,235)(115,234)(116,233)(117,240)(118,239)(119,238)(120,237);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(240)!(  2,  3)(  5, 17)(  6, 19)(  7, 18)(  8, 20)(  9, 13)( 10, 15)
( 11, 14)( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)
( 27, 58)( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)
( 35, 50)( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)
( 66, 79)( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)
( 90,115)( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)
( 98,107)( 99,106)(100,108)(122,123)(125,137)(126,139)(127,138)(128,140)
(129,133)(130,135)(131,134)(132,136)(141,161)(142,163)(143,162)(144,164)
(145,177)(146,179)(147,178)(148,180)(149,173)(150,175)(151,174)(152,176)
(153,169)(154,171)(155,170)(156,172)(157,165)(158,167)(159,166)(160,168)
(182,183)(185,197)(186,199)(187,198)(188,200)(189,193)(190,195)(191,194)
(192,196)(201,221)(202,223)(203,222)(204,224)(205,237)(206,239)(207,238)
(208,240)(209,233)(210,235)(211,234)(212,236)(213,229)(214,231)(215,230)
(216,232)(217,225)(218,227)(219,226)(220,228);
s1 := Sym(240)!(  1, 25)(  2, 26)(  3, 28)(  4, 27)(  5, 21)(  6, 22)(  7, 24)
(  8, 23)(  9, 37)( 10, 38)( 11, 40)( 12, 39)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 41, 45)( 42, 46)( 43, 48)
( 44, 47)( 49, 57)( 50, 58)( 51, 60)( 52, 59)( 55, 56)( 61, 85)( 62, 86)
( 63, 88)( 64, 87)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 97)( 70, 98)
( 71,100)( 72, 99)( 73, 93)( 74, 94)( 75, 96)( 76, 95)( 77, 89)( 78, 90)
( 79, 92)( 80, 91)(101,105)(102,106)(103,108)(104,107)(109,117)(110,118)
(111,120)(112,119)(115,116)(121,205)(122,206)(123,208)(124,207)(125,201)
(126,202)(127,204)(128,203)(129,217)(130,218)(131,220)(132,219)(133,213)
(134,214)(135,216)(136,215)(137,209)(138,210)(139,212)(140,211)(141,185)
(142,186)(143,188)(144,187)(145,181)(146,182)(147,184)(148,183)(149,197)
(150,198)(151,200)(152,199)(153,193)(154,194)(155,196)(156,195)(157,189)
(158,190)(159,192)(160,191)(161,225)(162,226)(163,228)(164,227)(165,221)
(166,222)(167,224)(168,223)(169,237)(170,238)(171,240)(172,239)(173,233)
(174,234)(175,236)(176,235)(177,229)(178,230)(179,232)(180,231);
s2 := Sym(240)!(  1,124)(  2,123)(  3,122)(  4,121)(  5,128)(  6,127)(  7,126)
(  8,125)(  9,132)( 10,131)( 11,130)( 12,129)( 13,136)( 14,135)( 15,134)
( 16,133)( 17,140)( 18,139)( 19,138)( 20,137)( 21,144)( 22,143)( 23,142)
( 24,141)( 25,148)( 26,147)( 27,146)( 28,145)( 29,152)( 30,151)( 31,150)
( 32,149)( 33,156)( 34,155)( 35,154)( 36,153)( 37,160)( 38,159)( 39,158)
( 40,157)( 41,164)( 42,163)( 43,162)( 44,161)( 45,168)( 46,167)( 47,166)
( 48,165)( 49,172)( 50,171)( 51,170)( 52,169)( 53,176)( 54,175)( 55,174)
( 56,173)( 57,180)( 58,179)( 59,178)( 60,177)( 61,184)( 62,183)( 63,182)
( 64,181)( 65,188)( 66,187)( 67,186)( 68,185)( 69,192)( 70,191)( 71,190)
( 72,189)( 73,196)( 74,195)( 75,194)( 76,193)( 77,200)( 78,199)( 79,198)
( 80,197)( 81,204)( 82,203)( 83,202)( 84,201)( 85,208)( 86,207)( 87,206)
( 88,205)( 89,212)( 90,211)( 91,210)( 92,209)( 93,216)( 94,215)( 95,214)
( 96,213)( 97,220)( 98,219)( 99,218)(100,217)(101,224)(102,223)(103,222)
(104,221)(105,228)(106,227)(107,226)(108,225)(109,232)(110,231)(111,230)
(112,229)(113,236)(114,235)(115,234)(116,233)(117,240)(118,239)(119,238)
(120,237);
poly := sub<Sym(240)|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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope