Simplest Canonical Polyhedron with C4 Symmetry (1 of 5)

C0 = 0.0692776715108154991415937259141
C1 = 0.284809449988155943373476836322
C2 = 0.617813400207904640433740350597
C3 = 0.743350816929515119782399383807
C4 = 0.786324743680082506910233551459
C5 = 0.902076883163452478503402036266
C6 = 1.017425061294311072057942196952

C0 = square-root of a root of the polynomial:  1297321*(x^16)
    - 866294088*(x^15) + 15635488432*(x^14) - 123139508848*(x^13)
    + 556934324172*(x^12) - 1617535376328*(x^11) + 3199642981744*(x^10)
    - 4460312754224*(x^9) + 4467795805702*(x^8) - 3242266551192*(x^7)
    + 1698898746640*(x^6) - 630490234320*(x^5) + 158173460204*(x^4)
    - 24167981912*(x^3) + 1712541904*(x^2) - 8671632*x + 4761
C1 = square-root of a root of the polynomial:  81*(x^16) + 25308*(x^15)
    + 2806756*(x^14) + 117844216*(x^13) + 928402440*(x^12) + 898197360*(x^11)
    + 1988872720*(x^10) + 15097498080*(x^9) + 58733145472*(x^8)
    + 107427370560*(x^7) + 106147656384*(x^6) + 4314319488*(x^5)
    - 68715561600*(x^4) - 25326100224*(x^3) - 1096291584*(x^2) + 201927168*x
    + 7278336
C2 = square-root of a root of the polynomial:  9*(x^16) - 1680*(x^15)
    + 113704*(x^14) - 3754744*(x^13) + 66511108*(x^12) - 652518032*(x^11)
    + 3639797032*(x^10) - 12490234296*(x^9) + 28294997182*(x^8)
    - 44665706672*(x^7) + 51023711416*(x^6) - 42821716392*(x^5)
    + 26064269780*(x^4) - 11112023088*(x^3) + 3111976440*(x^2) - 469831080*x
    + 21687649
C3 = square-root of a root of the polynomial:  81*(x^16) - 5760*(x^15)
    + 236152*(x^14) - 25739000*(x^13) + 1079102084*(x^12) - 9204552640*(x^11)
    + 38612442488*(x^10) - 100771449336*(x^9) + 186888743182*(x^8)
    - 271359198848*(x^7) + 320321746216*(x^6) - 295170099240*(x^5)
    + 197147649684*(x^4) - 90674026816*(x^3) + 28814720744*(x^2)
    - 6477875944*x + 825585289
C4 = square-root of a root of the polynomial:  9*(x^16) + 1536*(x^15)
    + 89584*(x^14) + 2334248*(x^13) + 27298480*(x^12) + 108120400*(x^11)
    - 113180240*(x^10) - 186376032*(x^9) + 429680752*(x^8) - 103710528*(x^7)
    - 315709248*(x^6) + 76374144*(x^5) + 268230528*(x^4) - 151932672*(x^3)
    - 58910976*(x^2) + 32099328*x + 7278336
C5 = square-root of a root of the polynomial:  81*(x^16) - 16380*(x^15)
    + 218740*(x^14) + 200166680*(x^13) - 284300408*(x^12) + 3322621840*(x^11)
    + 3148778704*(x^10) - 53856951456*(x^9) + 152719899520*(x^8)
    - 408189905472*(x^7) + 392197539264*(x^6) + 1529776780416*(x^5)
    - 754672505472*(x^4) - 457016649984*(x^3) - 12318863616*(x^2)
    + 463200768*x + 7278336
C6 = square-root of a root of the polynomial:  35027667*(x^16)
    + 23660873352*(x^15) + 22661836320*(x^14) - 1267787562624*(x^13)
    - 6845467909888*(x^12) - 14999826767360*(x^11) - 16583140928512*(x^10)
    - 7020164325376*(x^9) + 9001949253632*(x^8) + 16903613743104*(x^7)
    + 12807127236608*(x^6) + 5717156167680*(x^5) + 2273233600512*(x^4)
    + 3584355729408*(x^3) + 3140204101632*(x^2) + 1117060595712*x
    + 158997676032

V0  = ( C5,  C1,  C3)
V1  = (-C5, -C1,  C3)
V2  = ( C1, -C5,  C3)
V3  = (-C1,  C5,  C3)
V4  = ( C4,  C4, -C2)
V5  = ( C4, -C4, -C2)
V6  = (-C4,  C4, -C2)
V7  = (-C4, -C4, -C2)
V8  = ( C6, 0.0, -C0)
V9  = (-C6, 0.0, -C0)
V10 = (0.0,  C6, -C0)
V11 = (0.0, -C6, -C0)

Faces:
{  0,  3,  1,  2 }
{  4,  5,  7,  6 }
{  0,  4, 10,  3 }
{  3,  6,  9,  1 }
{  1,  7, 11,  2 }
{  2,  5,  8,  0 }
{  8,  5,  4 }
{  8,  4,  0 }
{  9,  6,  7 }
{  9,  7,  1 }
{ 10,  4,  6 }
{ 10,  6,  3 }
{ 11,  7,  5 }
{ 11,  5,  2 }
