Simplest Canonical Polyhedron with C3 Symmetry (1 of 5)

C0  = 0.0811612249576076575911648178180
C1  = 0.0972149341447479056804497731819
C2  = 0.361665828265210826385522284617
C3  = 0.518352616919316584671171078894
C4  = 0.5300470334583766598576183184853
C5  = 0.611333931309450978511133637591
C6  = 0.7236385240615732050915058783246
C7  = 0.791372746832825594881318993856
C8  = 0.820853458206321110771955651506
C9  = 0.891712861723587486243140603103
C10 = 0.8937837306664239218978792304748
C11 = 0.897813068740543178174115706336
C12 = 1.03670523383863316934234215779
C13 = 1.058861429418791126341962938954
C14 = 1.22266786261890195702226727518

C0  = square-root of a root of the polynomial:  1285404935049*(x^12)
    - 414052409486043*(x^11) + 3086575319479887*(x^10)
    - 11438981875689084*(x^9) + 26020830257244477*(x^8)
    - 36435589586476350*(x^7) + 31657937736233848*(x^6)
    - 18081926199526089*(x^5) + 6972203134691025*(x^4) - 1382547124642913*(x^3)
    - 30175550574207*(x^2) - 22892925726*x + 1842383929
C1  = square-root of a root of the polynomial:  729*(x^12) + 110565*(x^11)
    + 25897320*(x^10) + 44770374*(x^9) + 72013203*(x^8) + 3566060523*(x^7)
    + 15384377860*(x^6) + 20345961387*(x^5) + 18852897243*(x^4)
    + 16958730564*(x^3) + 55806534*(x^2) - 1741068*x - 2997
C2  = square-root of a root of the polynomial:  (x^12) + 534*(x^11)
    + 73574*(x^10) + 545588*(x^9) - 14136374*(x^8) + 28752353*(x^7)
    - 115448447*(x^6) + 1437446898*(x^5) + 5196789441*(x^4) + 4860089424*(x^3)
    + 118077588*(x^2) - 93940398*x - 2184813
C3  = square-root of a root of the polynomial:  1285404935049*(x^12)
    + 109440829190025*(x^11) + 35716269184956*(x^10) - 7055541329526*(x^9)
    - 2631723286365*(x^8) + 4123196223*(x^7) + 5266507540*(x^6)
    - 5170540845*(x^5) + 69148695*(x^4) - 4852080*(x^3) - 4212522*(x^2)
    - 88344*x - 2997
C4  = square-root of a root of the polynomial:  (x^12) - 251*(x^11)
    + 16204*(x^10) + 1581342*(x^9) + 13160293*(x^8) + 60948094*(x^7)
    + 80623060*(x^6) + 61465194*(x^5) - 648795123*(x^4) + 397320309*(x^3)
    + 106219674*(x^2) - 39595635*x - 2184813
C5  = square-root of a root of the polynomial:  6561*(x^12) + 582471*(x^11)
    + 15960564*(x^10) + 139208463*(x^9) - 17721936*(x^8) + 10623852*(x^7)
    + 26384722*(x^6) - 10624695*(x^5) + 2573679*(x^4) + 285840*(x^3)
    - 335484*(x^2) - 92151*x - 2997
C6  = square-root of a root of the polynomial:  729*(x^12) + 374463*(x^11)
    + 100001628*(x^10) + 5076667278*(x^9) - 78272634591*(x^8)
    + 952717523346*(x^7) - 2849858253008*(x^6) + 3214768149462*(x^5)
    + 54436517756157*(x^4) + 89806117798215*(x^3) - 1429045922070*(x^2)
    - 27173954827773*x - 2444744970837
C7  = square-root of a root of the polynomial:  6561*(x^12) - 661203*(x^11)
    + 22800771*(x^10) - 332293428*(x^9) + 2052735021*(x^8) - 6993032454*(x^7)
    + 14924930776*(x^6) - 21214982493*(x^5) + 20563968237*(x^4)
    - 13517764157*(x^3) + 5794573653*(x^2) - 1467133170*x + 166848889
C8  = square-root of a root of the polynomial:  729*(x^12) - 197802*(x^11)
    + 12446298*(x^10) + 4759626312*(x^9) + 25798719474*(x^8)
    - 79414005141*(x^7) - 260759812919*(x^6) + 5519421206202*(x^5)
    - 6593523162243*(x^4) + 5151025099044*(x^3) + 6295957607016*(x^2)
    - 4706204943330*x - 642433566357
C9  = square-root of a root of the polynomial:  (x^12) + 111*(x^11)
    + 99996*(x^10) + 12300630*(x^9) - 70196345*(x^8) + 810163197*(x^7)
    - 10535405400*(x^6) + 25643491353*(x^5) + 27927998019*(x^4)
    + 118818607752*(x^3) + 27401216058*(x^2) - 100021447728*x - 14334558093
C10 = square-root of a root of the polynomial:  729*(x^12) - 56619*(x^11)
    + 2532627*(x^10) - 58242132*(x^9) + 367688421*(x^8) - 1208384406*(x^7)
    + 2505212440*(x^6) - 3522030309*(x^5) + 3421565709*(x^4) - 2271548297*(x^3)
    + 993794049*(x^2) - 263586210*x + 33051001
C11 = square-root of a root of the polynomial:  1763244081*(x^12)
    + 450373782675*(x^11) + 440941594876*(x^10) - 261316345538*(x^9)
    - 292413698485*(x^8) + 1374398741*(x^7) + 5266507540*(x^6)
    - 15511622535*(x^5) + 622338255*(x^4) - 131006160*(x^3) - 341214282*(x^2)
    - 21467592*x - 2184813
C12 = square-root of a root of the polynomial:  1285404935049*(x^12)
    + 437763316760100*(x^11) + 571460306959296*(x^10) - 451554645089664*(x^9)
    - 673721161309440*(x^8) + 4222152932352*(x^7) + 21571614883840*(x^6)
    - 84714141204480*(x^5) + 4531728875520*(x^4) - 1271943659520*(x^3)
    - 4417149468672*(x^2) - 370541592576*x - 50281316352
C13 = square-root of a root of the polynomial:  9*(x^12) + 2397*(x^11)
    + 197044*(x^10) + 5155869*(x^9) - 1969104*(x^8) + 3541284*(x^7)
    + 26384722*(x^6) - 31874085*(x^5) + 23163111*(x^4) + 7717680*(x^3)
    - 27174204*(x^2) - 22392693*x - 2184813
C14 = square-root of a root of the polynomial:  6561*(x^12) + 2329884*(x^11)
    + 255369024*(x^10) + 8909341632*(x^9) - 4536815616*(x^8)
    + 10878824448*(x^7) + 108071821312*(x^6) - 174075002880*(x^5)
    + 168668626944*(x^4) + 74931240960*(x^3) - 351780470784*(x^2)
    - 386509307904*x - 50281316352

V0 = (  C1,   C9, C10)
V1 = ( -C8,  -C2, C10)
V2 = (  C6,  -C4, C10)
V3 = ( C14,  0.0, -C7)
V4 = ( -C5,  C13, -C7)
V5 = ( -C5, -C13, -C7)
V6 = (-C12,  0.0, -C0)
V7 = (  C3, -C11, -C0)
V8 = (  C3,  C11, -C0)

Faces:
{ 0, 4, 6, 1 }
{ 1, 5, 7, 2 }
{ 2, 3, 8, 0 }
{ 6, 4, 5 }
{ 6, 5, 1 }
{ 7, 5, 3 }
{ 7, 3, 2 }
{ 8, 3, 4 }
{ 8, 4, 0 }
{ 0, 1, 2 }
{ 3, 5, 4 }
