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# Polytope of Type {30,20}

Atlas Canonical Name : {30,20}*1200c
if this polytope has a name.
Group : SmallGroup(1200,856)
Rank : 3
Schlafli Type : {30,20}
Number of vertices, edges, etc : 30, 300, 20
Order of s0s1s2 : 60
Order of s0s1s2s1 : 10
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {30,10}*600c
3-fold quotients : {10,20}*400c
4-fold quotients : {15,10}*300
5-fold quotients : {30,4}*240a
6-fold quotients : {10,10}*200c
10-fold quotients : {30,2}*120
12-fold quotients : {5,10}*100
15-fold quotients : {10,4}*80
20-fold quotients : {15,2}*60
25-fold quotients : {6,4}*48a
30-fold quotients : {10,2}*40
50-fold quotients : {6,2}*24
60-fold quotients : {5,2}*20
75-fold quotients : {2,4}*16
100-fold quotients : {3,2}*12
150-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 51)( 27, 55)( 28, 54)( 29, 53)
( 30, 52)( 31, 71)( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 66)( 37, 70)
( 38, 69)( 39, 68)( 40, 67)( 41, 61)( 42, 65)( 43, 64)( 44, 63)( 45, 62)
( 46, 56)( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(101,126)(102,130)(103,129)(104,128)(105,127)(106,146)(107,150)
(108,149)(109,148)(110,147)(111,141)(112,145)(113,144)(114,143)(115,142)
(116,136)(117,140)(118,139)(119,138)(120,137)(121,131)(122,135)(123,134)
(124,133)(125,132)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)
(160,172)(161,166)(162,170)(163,169)(164,168)(165,167)(176,201)(177,205)
(178,204)(179,203)(180,202)(181,221)(182,225)(183,224)(184,223)(185,222)
(186,216)(187,220)(188,219)(189,218)(190,217)(191,211)(192,215)(193,214)
(194,213)(195,212)(196,206)(197,210)(198,209)(199,208)(200,207)(227,230)
(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)
(238,244)(239,243)(240,242)(251,276)(252,280)(253,279)(254,278)(255,277)
(256,296)(257,300)(258,299)(259,298)(260,297)(261,291)(262,295)(263,294)
(264,293)(265,292)(266,286)(267,290)(268,289)(269,288)(270,287)(271,281)
(272,285)(273,284)(274,283)(275,282);;
s1 := (  1,182)(  2,181)(  3,185)(  4,184)(  5,183)(  6,177)(  7,176)(  8,180)
(  9,179)( 10,178)( 11,197)( 12,196)( 13,200)( 14,199)( 15,198)( 16,192)
( 17,191)( 18,195)( 19,194)( 20,193)( 21,187)( 22,186)( 23,190)( 24,189)
( 25,188)( 26,157)( 27,156)( 28,160)( 29,159)( 30,158)( 31,152)( 32,151)
( 33,155)( 34,154)( 35,153)( 36,172)( 37,171)( 38,175)( 39,174)( 40,173)
( 41,167)( 42,166)( 43,170)( 44,169)( 45,168)( 46,162)( 47,161)( 48,165)
( 49,164)( 50,163)( 51,207)( 52,206)( 53,210)( 54,209)( 55,208)( 56,202)
( 57,201)( 58,205)( 59,204)( 60,203)( 61,222)( 62,221)( 63,225)( 64,224)
( 65,223)( 66,217)( 67,216)( 68,220)( 69,219)( 70,218)( 71,212)( 72,211)
( 73,215)( 74,214)( 75,213)( 76,257)( 77,256)( 78,260)( 79,259)( 80,258)
( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,272)( 87,271)( 88,275)
( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)( 96,262)
( 97,261)( 98,265)( 99,264)(100,263)(101,232)(102,231)(103,235)(104,234)
(105,233)(106,227)(107,226)(108,230)(109,229)(110,228)(111,247)(112,246)
(113,250)(114,249)(115,248)(116,242)(117,241)(118,245)(119,244)(120,243)
(121,237)(122,236)(123,240)(124,239)(125,238)(126,282)(127,281)(128,285)
(129,284)(130,283)(131,277)(132,276)(133,280)(134,279)(135,278)(136,297)
(137,296)(138,300)(139,299)(140,298)(141,292)(142,291)(143,295)(144,294)
(145,293)(146,287)(147,286)(148,290)(149,289)(150,288);;
s2 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)
(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)
(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)
(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)(153,229)(154,228)
(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)(161,236)(162,240)
(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)(169,243)(170,242)
(171,246)(172,250)(173,249)(174,248)(175,247)(176,251)(177,255)(178,254)
(179,253)(180,252)(181,256)(182,260)(183,259)(184,258)(185,257)(186,261)
(187,265)(188,264)(189,263)(190,262)(191,266)(192,270)(193,269)(194,268)
(195,267)(196,271)(197,275)(198,274)(199,273)(200,272)(201,276)(202,280)
(203,279)(204,278)(205,277)(206,281)(207,285)(208,284)(209,283)(210,282)
(211,286)(212,290)(213,289)(214,288)(215,287)(216,291)(217,295)(218,294)
(219,293)(220,292)(221,296)(222,300)(223,299)(224,298)(225,297);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(300)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)
( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 26, 51)( 27, 55)( 28, 54)
( 29, 53)( 30, 52)( 31, 71)( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 66)
( 37, 70)( 38, 69)( 39, 68)( 40, 67)( 41, 61)( 42, 65)( 43, 64)( 44, 63)
( 45, 62)( 46, 56)( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 77, 80)( 78, 79)
( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)
( 89, 93)( 90, 92)(101,126)(102,130)(103,129)(104,128)(105,127)(106,146)
(107,150)(108,149)(109,148)(110,147)(111,141)(112,145)(113,144)(114,143)
(115,142)(116,136)(117,140)(118,139)(119,138)(120,137)(121,131)(122,135)
(123,134)(124,133)(125,132)(152,155)(153,154)(156,171)(157,175)(158,174)
(159,173)(160,172)(161,166)(162,170)(163,169)(164,168)(165,167)(176,201)
(177,205)(178,204)(179,203)(180,202)(181,221)(182,225)(183,224)(184,223)
(185,222)(186,216)(187,220)(188,219)(189,218)(190,217)(191,211)(192,215)
(193,214)(194,213)(195,212)(196,206)(197,210)(198,209)(199,208)(200,207)
(227,230)(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)
(237,245)(238,244)(239,243)(240,242)(251,276)(252,280)(253,279)(254,278)
(255,277)(256,296)(257,300)(258,299)(259,298)(260,297)(261,291)(262,295)
(263,294)(264,293)(265,292)(266,286)(267,290)(268,289)(269,288)(270,287)
(271,281)(272,285)(273,284)(274,283)(275,282);
s1 := Sym(300)!(  1,182)(  2,181)(  3,185)(  4,184)(  5,183)(  6,177)(  7,176)
(  8,180)(  9,179)( 10,178)( 11,197)( 12,196)( 13,200)( 14,199)( 15,198)
( 16,192)( 17,191)( 18,195)( 19,194)( 20,193)( 21,187)( 22,186)( 23,190)
( 24,189)( 25,188)( 26,157)( 27,156)( 28,160)( 29,159)( 30,158)( 31,152)
( 32,151)( 33,155)( 34,154)( 35,153)( 36,172)( 37,171)( 38,175)( 39,174)
( 40,173)( 41,167)( 42,166)( 43,170)( 44,169)( 45,168)( 46,162)( 47,161)
( 48,165)( 49,164)( 50,163)( 51,207)( 52,206)( 53,210)( 54,209)( 55,208)
( 56,202)( 57,201)( 58,205)( 59,204)( 60,203)( 61,222)( 62,221)( 63,225)
( 64,224)( 65,223)( 66,217)( 67,216)( 68,220)( 69,219)( 70,218)( 71,212)
( 72,211)( 73,215)( 74,214)( 75,213)( 76,257)( 77,256)( 78,260)( 79,259)
( 80,258)( 81,252)( 82,251)( 83,255)( 84,254)( 85,253)( 86,272)( 87,271)
( 88,275)( 89,274)( 90,273)( 91,267)( 92,266)( 93,270)( 94,269)( 95,268)
( 96,262)( 97,261)( 98,265)( 99,264)(100,263)(101,232)(102,231)(103,235)
(104,234)(105,233)(106,227)(107,226)(108,230)(109,229)(110,228)(111,247)
(112,246)(113,250)(114,249)(115,248)(116,242)(117,241)(118,245)(119,244)
(120,243)(121,237)(122,236)(123,240)(124,239)(125,238)(126,282)(127,281)
(128,285)(129,284)(130,283)(131,277)(132,276)(133,280)(134,279)(135,278)
(136,297)(137,296)(138,300)(139,299)(140,298)(141,292)(142,291)(143,295)
(144,294)(145,293)(146,287)(147,286)(148,290)(149,289)(150,288);
s2 := Sym(300)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)
(118,119)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)
(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)(153,229)
(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)(161,236)
(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)(169,243)
(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)(176,251)(177,255)
(178,254)(179,253)(180,252)(181,256)(182,260)(183,259)(184,258)(185,257)
(186,261)(187,265)(188,264)(189,263)(190,262)(191,266)(192,270)(193,269)
(194,268)(195,267)(196,271)(197,275)(198,274)(199,273)(200,272)(201,276)
(202,280)(203,279)(204,278)(205,277)(206,281)(207,285)(208,284)(209,283)
(210,282)(211,286)(212,290)(213,289)(214,288)(215,287)(216,291)(217,295)
(218,294)(219,293)(220,292)(221,296)(222,300)(223,299)(224,298)(225,297);
poly := sub<Sym(300)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope