# Polytope of Type {102,4}

Atlas Canonical Name : {102,4}*816c
if this polytope has a name.
Group : SmallGroup(816,195)
Rank : 3
Schlafli Type : {102,4}
Number of vertices, edges, etc : 102, 204, 4
Order of s0s1s2 : 51
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{102,4,2} of size 1632
Vertex Figure Of :
{2,102,4} of size 1632
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {51,4}*408
17-fold quotients : {6,4}*48b
34-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {102,4}*1632
Permutation Representation (GAP) :
```s0 := (  2,  3)(  5, 65)(  6, 67)(  7, 66)(  8, 68)(  9, 61)( 10, 63)( 11, 62)
( 12, 64)( 13, 57)( 14, 59)( 15, 58)( 16, 60)( 17, 53)( 18, 55)( 19, 54)
( 20, 56)( 21, 49)( 22, 51)( 23, 50)( 24, 52)( 25, 45)( 26, 47)( 27, 46)
( 28, 48)( 29, 41)( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)( 35, 38)
( 36, 40)( 69,137)( 70,139)( 71,138)( 72,140)( 73,201)( 74,203)( 75,202)
( 76,204)( 77,197)( 78,199)( 79,198)( 80,200)( 81,193)( 82,195)( 83,194)
( 84,196)( 85,189)( 86,191)( 87,190)( 88,192)( 89,185)( 90,187)( 91,186)
( 92,188)( 93,181)( 94,183)( 95,182)( 96,184)( 97,177)( 98,179)( 99,178)
(100,180)(101,173)(102,175)(103,174)(104,176)(105,169)(106,171)(107,170)
(108,172)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)(115,162)
(116,164)(117,157)(118,159)(119,158)(120,160)(121,153)(122,155)(123,154)
(124,156)(125,149)(126,151)(127,150)(128,152)(129,145)(130,147)(131,146)
(132,148)(133,141)(134,143)(135,142)(136,144)(206,207)(209,269)(210,271)
(211,270)(212,272)(213,265)(214,267)(215,266)(216,268)(217,261)(218,263)
(219,262)(220,264)(221,257)(222,259)(223,258)(224,260)(225,253)(226,255)
(227,254)(228,256)(229,249)(230,251)(231,250)(232,252)(233,245)(234,247)
(235,246)(236,248)(237,241)(238,243)(239,242)(240,244)(273,341)(274,343)
(275,342)(276,344)(277,405)(278,407)(279,406)(280,408)(281,401)(282,403)
(283,402)(284,404)(285,397)(286,399)(287,398)(288,400)(289,393)(290,395)
(291,394)(292,396)(293,389)(294,391)(295,390)(296,392)(297,385)(298,387)
(299,386)(300,388)(301,381)(302,383)(303,382)(304,384)(305,377)(306,379)
(307,378)(308,380)(309,373)(310,375)(311,374)(312,376)(313,369)(314,371)
(315,370)(316,372)(317,365)(318,367)(319,366)(320,368)(321,361)(322,363)
(323,362)(324,364)(325,357)(326,359)(327,358)(328,360)(329,353)(330,355)
(331,354)(332,356)(333,349)(334,351)(335,350)(336,352)(337,345)(338,347)
(339,346)(340,348);;
s1 := (  1,277)(  2,278)(  3,280)(  4,279)(  5,273)(  6,274)(  7,276)(  8,275)
(  9,337)( 10,338)( 11,340)( 12,339)( 13,333)( 14,334)( 15,336)( 16,335)
( 17,329)( 18,330)( 19,332)( 20,331)( 21,325)( 22,326)( 23,328)( 24,327)
( 25,321)( 26,322)( 27,324)( 28,323)( 29,317)( 30,318)( 31,320)( 32,319)
( 33,313)( 34,314)( 35,316)( 36,315)( 37,309)( 38,310)( 39,312)( 40,311)
( 41,305)( 42,306)( 43,308)( 44,307)( 45,301)( 46,302)( 47,304)( 48,303)
( 49,297)( 50,298)( 51,300)( 52,299)( 53,293)( 54,294)( 55,296)( 56,295)
( 57,289)( 58,290)( 59,292)( 60,291)( 61,285)( 62,286)( 63,288)( 64,287)
( 65,281)( 66,282)( 67,284)( 68,283)( 69,209)( 70,210)( 71,212)( 72,211)
( 73,205)( 74,206)( 75,208)( 76,207)( 77,269)( 78,270)( 79,272)( 80,271)
( 81,265)( 82,266)( 83,268)( 84,267)( 85,261)( 86,262)( 87,264)( 88,263)
( 89,257)( 90,258)( 91,260)( 92,259)( 93,253)( 94,254)( 95,256)( 96,255)
( 97,249)( 98,250)( 99,252)(100,251)(101,245)(102,246)(103,248)(104,247)
(105,241)(106,242)(107,244)(108,243)(109,237)(110,238)(111,240)(112,239)
(113,233)(114,234)(115,236)(116,235)(117,229)(118,230)(119,232)(120,231)
(121,225)(122,226)(123,228)(124,227)(125,221)(126,222)(127,224)(128,223)
(129,217)(130,218)(131,220)(132,219)(133,213)(134,214)(135,216)(136,215)
(137,345)(138,346)(139,348)(140,347)(141,341)(142,342)(143,344)(144,343)
(145,405)(146,406)(147,408)(148,407)(149,401)(150,402)(151,404)(152,403)
(153,397)(154,398)(155,400)(156,399)(157,393)(158,394)(159,396)(160,395)
(161,389)(162,390)(163,392)(164,391)(165,385)(166,386)(167,388)(168,387)
(169,381)(170,382)(171,384)(172,383)(173,377)(174,378)(175,380)(176,379)
(177,373)(178,374)(179,376)(180,375)(181,369)(182,370)(183,372)(184,371)
(185,365)(186,366)(187,368)(188,367)(189,361)(190,362)(191,364)(192,363)
(193,357)(194,358)(195,360)(196,359)(197,353)(198,354)(199,356)(200,355)
(201,349)(202,350)(203,352)(204,351);;
s2 := (  1,208)(  2,207)(  3,206)(  4,205)(  5,212)(  6,211)(  7,210)(  8,209)
(  9,216)( 10,215)( 11,214)( 12,213)( 13,220)( 14,219)( 15,218)( 16,217)
( 17,224)( 18,223)( 19,222)( 20,221)( 21,228)( 22,227)( 23,226)( 24,225)
( 25,232)( 26,231)( 27,230)( 28,229)( 29,236)( 30,235)( 31,234)( 32,233)
( 33,240)( 34,239)( 35,238)( 36,237)( 37,244)( 38,243)( 39,242)( 40,241)
( 41,248)( 42,247)( 43,246)( 44,245)( 45,252)( 46,251)( 47,250)( 48,249)
( 49,256)( 50,255)( 51,254)( 52,253)( 53,260)( 54,259)( 55,258)( 56,257)
( 57,264)( 58,263)( 59,262)( 60,261)( 61,268)( 62,267)( 63,266)( 64,265)
( 65,272)( 66,271)( 67,270)( 68,269)( 69,276)( 70,275)( 71,274)( 72,273)
( 73,280)( 74,279)( 75,278)( 76,277)( 77,284)( 78,283)( 79,282)( 80,281)
( 81,288)( 82,287)( 83,286)( 84,285)( 85,292)( 86,291)( 87,290)( 88,289)
( 89,296)( 90,295)( 91,294)( 92,293)( 93,300)( 94,299)( 95,298)( 96,297)
( 97,304)( 98,303)( 99,302)(100,301)(101,308)(102,307)(103,306)(104,305)
(105,312)(106,311)(107,310)(108,309)(109,316)(110,315)(111,314)(112,313)
(113,320)(114,319)(115,318)(116,317)(117,324)(118,323)(119,322)(120,321)
(121,328)(122,327)(123,326)(124,325)(125,332)(126,331)(127,330)(128,329)
(129,336)(130,335)(131,334)(132,333)(133,340)(134,339)(135,338)(136,337)
(137,344)(138,343)(139,342)(140,341)(141,348)(142,347)(143,346)(144,345)
(145,352)(146,351)(147,350)(148,349)(149,356)(150,355)(151,354)(152,353)
(153,360)(154,359)(155,358)(156,357)(157,364)(158,363)(159,362)(160,361)
(161,368)(162,367)(163,366)(164,365)(165,372)(166,371)(167,370)(168,369)
(169,376)(170,375)(171,374)(172,373)(173,380)(174,379)(175,378)(176,377)
(177,384)(178,383)(179,382)(180,381)(181,388)(182,387)(183,386)(184,385)
(185,392)(186,391)(187,390)(188,389)(189,396)(190,395)(191,394)(192,393)
(193,400)(194,399)(195,398)(196,397)(197,404)(198,403)(199,402)(200,401)
(201,408)(202,407)(203,406)(204,405);;
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*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*s2*s1*s0*s2*s1*s0*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 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(408)!(  2,  3)(  5, 65)(  6, 67)(  7, 66)(  8, 68)(  9, 61)( 10, 63)
( 11, 62)( 12, 64)( 13, 57)( 14, 59)( 15, 58)( 16, 60)( 17, 53)( 18, 55)
( 19, 54)( 20, 56)( 21, 49)( 22, 51)( 23, 50)( 24, 52)( 25, 45)( 26, 47)
( 27, 46)( 28, 48)( 29, 41)( 30, 43)( 31, 42)( 32, 44)( 33, 37)( 34, 39)
( 35, 38)( 36, 40)( 69,137)( 70,139)( 71,138)( 72,140)( 73,201)( 74,203)
( 75,202)( 76,204)( 77,197)( 78,199)( 79,198)( 80,200)( 81,193)( 82,195)
( 83,194)( 84,196)( 85,189)( 86,191)( 87,190)( 88,192)( 89,185)( 90,187)
( 91,186)( 92,188)( 93,181)( 94,183)( 95,182)( 96,184)( 97,177)( 98,179)
( 99,178)(100,180)(101,173)(102,175)(103,174)(104,176)(105,169)(106,171)
(107,170)(108,172)(109,165)(110,167)(111,166)(112,168)(113,161)(114,163)
(115,162)(116,164)(117,157)(118,159)(119,158)(120,160)(121,153)(122,155)
(123,154)(124,156)(125,149)(126,151)(127,150)(128,152)(129,145)(130,147)
(131,146)(132,148)(133,141)(134,143)(135,142)(136,144)(206,207)(209,269)
(210,271)(211,270)(212,272)(213,265)(214,267)(215,266)(216,268)(217,261)
(218,263)(219,262)(220,264)(221,257)(222,259)(223,258)(224,260)(225,253)
(226,255)(227,254)(228,256)(229,249)(230,251)(231,250)(232,252)(233,245)
(234,247)(235,246)(236,248)(237,241)(238,243)(239,242)(240,244)(273,341)
(274,343)(275,342)(276,344)(277,405)(278,407)(279,406)(280,408)(281,401)
(282,403)(283,402)(284,404)(285,397)(286,399)(287,398)(288,400)(289,393)
(290,395)(291,394)(292,396)(293,389)(294,391)(295,390)(296,392)(297,385)
(298,387)(299,386)(300,388)(301,381)(302,383)(303,382)(304,384)(305,377)
(306,379)(307,378)(308,380)(309,373)(310,375)(311,374)(312,376)(313,369)
(314,371)(315,370)(316,372)(317,365)(318,367)(319,366)(320,368)(321,361)
(322,363)(323,362)(324,364)(325,357)(326,359)(327,358)(328,360)(329,353)
(330,355)(331,354)(332,356)(333,349)(334,351)(335,350)(336,352)(337,345)
(338,347)(339,346)(340,348);
s1 := Sym(408)!(  1,277)(  2,278)(  3,280)(  4,279)(  5,273)(  6,274)(  7,276)
(  8,275)(  9,337)( 10,338)( 11,340)( 12,339)( 13,333)( 14,334)( 15,336)
( 16,335)( 17,329)( 18,330)( 19,332)( 20,331)( 21,325)( 22,326)( 23,328)
( 24,327)( 25,321)( 26,322)( 27,324)( 28,323)( 29,317)( 30,318)( 31,320)
( 32,319)( 33,313)( 34,314)( 35,316)( 36,315)( 37,309)( 38,310)( 39,312)
( 40,311)( 41,305)( 42,306)( 43,308)( 44,307)( 45,301)( 46,302)( 47,304)
( 48,303)( 49,297)( 50,298)( 51,300)( 52,299)( 53,293)( 54,294)( 55,296)
( 56,295)( 57,289)( 58,290)( 59,292)( 60,291)( 61,285)( 62,286)( 63,288)
( 64,287)( 65,281)( 66,282)( 67,284)( 68,283)( 69,209)( 70,210)( 71,212)
( 72,211)( 73,205)( 74,206)( 75,208)( 76,207)( 77,269)( 78,270)( 79,272)
( 80,271)( 81,265)( 82,266)( 83,268)( 84,267)( 85,261)( 86,262)( 87,264)
( 88,263)( 89,257)( 90,258)( 91,260)( 92,259)( 93,253)( 94,254)( 95,256)
( 96,255)( 97,249)( 98,250)( 99,252)(100,251)(101,245)(102,246)(103,248)
(104,247)(105,241)(106,242)(107,244)(108,243)(109,237)(110,238)(111,240)
(112,239)(113,233)(114,234)(115,236)(116,235)(117,229)(118,230)(119,232)
(120,231)(121,225)(122,226)(123,228)(124,227)(125,221)(126,222)(127,224)
(128,223)(129,217)(130,218)(131,220)(132,219)(133,213)(134,214)(135,216)
(136,215)(137,345)(138,346)(139,348)(140,347)(141,341)(142,342)(143,344)
(144,343)(145,405)(146,406)(147,408)(148,407)(149,401)(150,402)(151,404)
(152,403)(153,397)(154,398)(155,400)(156,399)(157,393)(158,394)(159,396)
(160,395)(161,389)(162,390)(163,392)(164,391)(165,385)(166,386)(167,388)
(168,387)(169,381)(170,382)(171,384)(172,383)(173,377)(174,378)(175,380)
(176,379)(177,373)(178,374)(179,376)(180,375)(181,369)(182,370)(183,372)
(184,371)(185,365)(186,366)(187,368)(188,367)(189,361)(190,362)(191,364)
(192,363)(193,357)(194,358)(195,360)(196,359)(197,353)(198,354)(199,356)
(200,355)(201,349)(202,350)(203,352)(204,351);
s2 := Sym(408)!(  1,208)(  2,207)(  3,206)(  4,205)(  5,212)(  6,211)(  7,210)
(  8,209)(  9,216)( 10,215)( 11,214)( 12,213)( 13,220)( 14,219)( 15,218)
( 16,217)( 17,224)( 18,223)( 19,222)( 20,221)( 21,228)( 22,227)( 23,226)
( 24,225)( 25,232)( 26,231)( 27,230)( 28,229)( 29,236)( 30,235)( 31,234)
( 32,233)( 33,240)( 34,239)( 35,238)( 36,237)( 37,244)( 38,243)( 39,242)
( 40,241)( 41,248)( 42,247)( 43,246)( 44,245)( 45,252)( 46,251)( 47,250)
( 48,249)( 49,256)( 50,255)( 51,254)( 52,253)( 53,260)( 54,259)( 55,258)
( 56,257)( 57,264)( 58,263)( 59,262)( 60,261)( 61,268)( 62,267)( 63,266)
( 64,265)( 65,272)( 66,271)( 67,270)( 68,269)( 69,276)( 70,275)( 71,274)
( 72,273)( 73,280)( 74,279)( 75,278)( 76,277)( 77,284)( 78,283)( 79,282)
( 80,281)( 81,288)( 82,287)( 83,286)( 84,285)( 85,292)( 86,291)( 87,290)
( 88,289)( 89,296)( 90,295)( 91,294)( 92,293)( 93,300)( 94,299)( 95,298)
( 96,297)( 97,304)( 98,303)( 99,302)(100,301)(101,308)(102,307)(103,306)
(104,305)(105,312)(106,311)(107,310)(108,309)(109,316)(110,315)(111,314)
(112,313)(113,320)(114,319)(115,318)(116,317)(117,324)(118,323)(119,322)
(120,321)(121,328)(122,327)(123,326)(124,325)(125,332)(126,331)(127,330)
(128,329)(129,336)(130,335)(131,334)(132,333)(133,340)(134,339)(135,338)
(136,337)(137,344)(138,343)(139,342)(140,341)(141,348)(142,347)(143,346)
(144,345)(145,352)(146,351)(147,350)(148,349)(149,356)(150,355)(151,354)
(152,353)(153,360)(154,359)(155,358)(156,357)(157,364)(158,363)(159,362)
(160,361)(161,368)(162,367)(163,366)(164,365)(165,372)(166,371)(167,370)
(168,369)(169,376)(170,375)(171,374)(172,373)(173,380)(174,379)(175,378)
(176,377)(177,384)(178,383)(179,382)(180,381)(181,388)(182,387)(183,386)
(184,385)(185,392)(186,391)(187,390)(188,389)(189,396)(190,395)(191,394)
(192,393)(193,400)(194,399)(195,398)(196,397)(197,404)(198,403)(199,402)
(200,401)(201,408)(202,407)(203,406)(204,405);
poly := sub<Sym(408)|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*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*s2*s1*s0*s2*s1*s0*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 >;

```
References : None.
to this polytope