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# Polytope of Type {38,20}

Atlas Canonical Name : {38,20}*1520
Also Known As : {38,20|2}. if this polytope has another name.
Group : SmallGroup(1520,120)
Rank : 3
Schlafli Type : {38,20}
Number of vertices, edges, etc : 38, 380, 20
Order of s0s1s2 : 380
Order of s0s1s2s1 : 2
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 : {38,10}*760
5-fold quotients : {38,4}*304
10-fold quotients : {38,2}*152
19-fold quotients : {2,20}*80
20-fold quotients : {19,2}*76
38-fold quotients : {2,10}*40
76-fold quotients : {2,5}*20
95-fold quotients : {2,4}*16
190-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)( 81, 92)
( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)( 99,112)
(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)(117,132)
(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(135,152)
(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(143,144)
(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)
(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)
(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)(215,224)
(216,223)(217,222)(218,221)(219,220)(230,247)(231,246)(232,245)(233,244)
(234,243)(235,242)(236,241)(237,240)(238,239)(249,266)(250,265)(251,264)
(252,263)(253,262)(254,261)(255,260)(256,259)(257,258)(268,285)(269,284)
(270,283)(271,282)(272,281)(273,280)(274,279)(275,278)(276,277)(287,304)
(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)
(306,323)(307,322)(308,321)(309,320)(310,319)(311,318)(312,317)(313,316)
(314,315)(325,342)(326,341)(327,340)(328,339)(329,338)(330,337)(331,336)
(332,335)(333,334)(344,361)(345,360)(346,359)(347,358)(348,357)(349,356)
(350,355)(351,354)(352,353)(363,380)(364,379)(365,378)(366,377)(367,376)
(368,375)(369,374)(370,373)(371,372);;
s1 := (  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)(  9, 13)
( 10, 12)( 20, 78)( 21, 77)( 22, 95)( 23, 94)( 24, 93)( 25, 92)( 26, 91)
( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33, 84)( 34, 83)
( 35, 82)( 36, 81)( 37, 80)( 38, 79)( 39, 59)( 40, 58)( 41, 76)( 42, 75)
( 43, 74)( 44, 73)( 45, 72)( 46, 71)( 47, 70)( 48, 69)( 49, 68)( 50, 67)
( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 57, 60)( 96, 97)
( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(115,173)(116,172)(117,190)(118,189)(119,188)(120,187)(121,186)(122,185)
(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)(130,177)
(131,176)(132,175)(133,174)(134,154)(135,153)(136,171)(137,170)(138,169)
(139,168)(140,167)(141,166)(142,165)(143,164)(144,163)(145,162)(146,161)
(147,160)(148,159)(149,158)(150,157)(151,156)(152,155)(191,287)(192,286)
(193,304)(194,303)(195,302)(196,301)(197,300)(198,299)(199,298)(200,297)
(201,296)(202,295)(203,294)(204,293)(205,292)(206,291)(207,290)(208,289)
(209,288)(210,363)(211,362)(212,380)(213,379)(214,378)(215,377)(216,376)
(217,375)(218,374)(219,373)(220,372)(221,371)(222,370)(223,369)(224,368)
(225,367)(226,366)(227,365)(228,364)(229,344)(230,343)(231,361)(232,360)
(233,359)(234,358)(235,357)(236,356)(237,355)(238,354)(239,353)(240,352)
(241,351)(242,350)(243,349)(244,348)(245,347)(246,346)(247,345)(248,325)
(249,324)(250,342)(251,341)(252,340)(253,339)(254,338)(255,337)(256,336)
(257,335)(258,334)(259,333)(260,332)(261,331)(262,330)(263,329)(264,328)
(265,327)(266,326)(267,306)(268,305)(269,323)(270,322)(271,321)(272,320)
(273,319)(274,318)(275,317)(276,316)(277,315)(278,314)(279,313)(280,312)
(281,311)(282,310)(283,309)(284,308)(285,307);;
s2 := (  1,210)(  2,211)(  3,212)(  4,213)(  5,214)(  6,215)(  7,216)(  8,217)
(  9,218)( 10,219)( 11,220)( 12,221)( 13,222)( 14,223)( 15,224)( 16,225)
( 17,226)( 18,227)( 19,228)( 20,191)( 21,192)( 22,193)( 23,194)( 24,195)
( 25,196)( 26,197)( 27,198)( 28,199)( 29,200)( 30,201)( 31,202)( 32,203)
( 33,204)( 34,205)( 35,206)( 36,207)( 37,208)( 38,209)( 39,267)( 40,268)
( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)( 48,276)
( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)( 56,284)
( 57,285)( 58,248)( 59,249)( 60,250)( 61,251)( 62,252)( 63,253)( 64,254)
( 65,255)( 66,256)( 67,257)( 68,258)( 69,259)( 70,260)( 71,261)( 72,262)
( 73,263)( 74,264)( 75,265)( 76,266)( 77,229)( 78,230)( 79,231)( 80,232)
( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)( 88,240)
( 89,241)( 90,242)( 91,243)( 92,244)( 93,245)( 94,246)( 95,247)( 96,305)
( 97,306)( 98,307)( 99,308)(100,309)(101,310)(102,311)(103,312)(104,313)
(105,314)(106,315)(107,316)(108,317)(109,318)(110,319)(111,320)(112,321)
(113,322)(114,323)(115,286)(116,287)(117,288)(118,289)(119,290)(120,291)
(121,292)(122,293)(123,294)(124,295)(125,296)(126,297)(127,298)(128,299)
(129,300)(130,301)(131,302)(132,303)(133,304)(134,362)(135,363)(136,364)
(137,365)(138,366)(139,367)(140,368)(141,369)(142,370)(143,371)(144,372)
(145,373)(146,374)(147,375)(148,376)(149,377)(150,378)(151,379)(152,380)
(153,343)(154,344)(155,345)(156,346)(157,347)(158,348)(159,349)(160,350)
(161,351)(162,352)(163,353)(164,354)(165,355)(166,356)(167,357)(168,358)
(169,359)(170,360)(171,361)(172,324)(173,325)(174,326)(175,327)(176,328)
(177,329)(178,330)(179,331)(180,332)(181,333)(182,334)(183,335)(184,336)
(185,337)(186,338)(187,339)(188,340)(189,341)(190,342);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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(380)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)
( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)
( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(116,133)
(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)
(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)
(143,144)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)
(161,164)(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)
(179,184)(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)
(197,204)(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)
(215,224)(216,223)(217,222)(218,221)(219,220)(230,247)(231,246)(232,245)
(233,244)(234,243)(235,242)(236,241)(237,240)(238,239)(249,266)(250,265)
(251,264)(252,263)(253,262)(254,261)(255,260)(256,259)(257,258)(268,285)
(269,284)(270,283)(271,282)(272,281)(273,280)(274,279)(275,278)(276,277)
(287,304)(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)
(295,296)(306,323)(307,322)(308,321)(309,320)(310,319)(311,318)(312,317)
(313,316)(314,315)(325,342)(326,341)(327,340)(328,339)(329,338)(330,337)
(331,336)(332,335)(333,334)(344,361)(345,360)(346,359)(347,358)(348,357)
(349,356)(350,355)(351,354)(352,353)(363,380)(364,379)(365,378)(366,377)
(367,376)(368,375)(369,374)(370,373)(371,372);
s1 := Sym(380)!(  1,  2)(  3, 19)(  4, 18)(  5, 17)(  6, 16)(  7, 15)(  8, 14)
(  9, 13)( 10, 12)( 20, 78)( 21, 77)( 22, 95)( 23, 94)( 24, 93)( 25, 92)
( 26, 91)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31, 86)( 32, 85)( 33, 84)
( 34, 83)( 35, 82)( 36, 81)( 37, 80)( 38, 79)( 39, 59)( 40, 58)( 41, 76)
( 42, 75)( 43, 74)( 44, 73)( 45, 72)( 46, 71)( 47, 70)( 48, 69)( 49, 68)
( 50, 67)( 51, 66)( 52, 65)( 53, 64)( 54, 63)( 55, 62)( 56, 61)( 57, 60)
( 96, 97)( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)
(105,107)(115,173)(116,172)(117,190)(118,189)(119,188)(120,187)(121,186)
(122,185)(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)
(130,177)(131,176)(132,175)(133,174)(134,154)(135,153)(136,171)(137,170)
(138,169)(139,168)(140,167)(141,166)(142,165)(143,164)(144,163)(145,162)
(146,161)(147,160)(148,159)(149,158)(150,157)(151,156)(152,155)(191,287)
(192,286)(193,304)(194,303)(195,302)(196,301)(197,300)(198,299)(199,298)
(200,297)(201,296)(202,295)(203,294)(204,293)(205,292)(206,291)(207,290)
(208,289)(209,288)(210,363)(211,362)(212,380)(213,379)(214,378)(215,377)
(216,376)(217,375)(218,374)(219,373)(220,372)(221,371)(222,370)(223,369)
(224,368)(225,367)(226,366)(227,365)(228,364)(229,344)(230,343)(231,361)
(232,360)(233,359)(234,358)(235,357)(236,356)(237,355)(238,354)(239,353)
(240,352)(241,351)(242,350)(243,349)(244,348)(245,347)(246,346)(247,345)
(248,325)(249,324)(250,342)(251,341)(252,340)(253,339)(254,338)(255,337)
(256,336)(257,335)(258,334)(259,333)(260,332)(261,331)(262,330)(263,329)
(264,328)(265,327)(266,326)(267,306)(268,305)(269,323)(270,322)(271,321)
(272,320)(273,319)(274,318)(275,317)(276,316)(277,315)(278,314)(279,313)
(280,312)(281,311)(282,310)(283,309)(284,308)(285,307);
s2 := Sym(380)!(  1,210)(  2,211)(  3,212)(  4,213)(  5,214)(  6,215)(  7,216)
(  8,217)(  9,218)( 10,219)( 11,220)( 12,221)( 13,222)( 14,223)( 15,224)
( 16,225)( 17,226)( 18,227)( 19,228)( 20,191)( 21,192)( 22,193)( 23,194)
( 24,195)( 25,196)( 26,197)( 27,198)( 28,199)( 29,200)( 30,201)( 31,202)
( 32,203)( 33,204)( 34,205)( 35,206)( 36,207)( 37,208)( 38,209)( 39,267)
( 40,268)( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)
( 48,276)( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)
( 56,284)( 57,285)( 58,248)( 59,249)( 60,250)( 61,251)( 62,252)( 63,253)
( 64,254)( 65,255)( 66,256)( 67,257)( 68,258)( 69,259)( 70,260)( 71,261)
( 72,262)( 73,263)( 74,264)( 75,265)( 76,266)( 77,229)( 78,230)( 79,231)
( 80,232)( 81,233)( 82,234)( 83,235)( 84,236)( 85,237)( 86,238)( 87,239)
( 88,240)( 89,241)( 90,242)( 91,243)( 92,244)( 93,245)( 94,246)( 95,247)
( 96,305)( 97,306)( 98,307)( 99,308)(100,309)(101,310)(102,311)(103,312)
(104,313)(105,314)(106,315)(107,316)(108,317)(109,318)(110,319)(111,320)
(112,321)(113,322)(114,323)(115,286)(116,287)(117,288)(118,289)(119,290)
(120,291)(121,292)(122,293)(123,294)(124,295)(125,296)(126,297)(127,298)
(128,299)(129,300)(130,301)(131,302)(132,303)(133,304)(134,362)(135,363)
(136,364)(137,365)(138,366)(139,367)(140,368)(141,369)(142,370)(143,371)
(144,372)(145,373)(146,374)(147,375)(148,376)(149,377)(150,378)(151,379)
(152,380)(153,343)(154,344)(155,345)(156,346)(157,347)(158,348)(159,349)
(160,350)(161,351)(162,352)(163,353)(164,354)(165,355)(166,356)(167,357)
(168,358)(169,359)(170,360)(171,361)(172,324)(173,325)(174,326)(175,327)
(176,328)(177,329)(178,330)(179,331)(180,332)(181,333)(182,334)(183,335)
(184,336)(185,337)(186,338)(187,339)(188,340)(189,341)(190,342);
poly := sub<Sym(380)|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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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