Hexagonal Trapezohedron Toroid

C0  = 0.114628621270660658681483427177  = sqrt(11 * sqrt(3) - 19) / 22
C1  = 0.176057914268593735164115078380  = sqrt(787 * sqrt(3) - 1363) / 2
C2  = 0.189468690981505999703046686857  = (2 * sqrt(2) - sqrt(6)) / 2
C3  = 0.258819045102520762348898837624  = (sqrt(6) - sqrt(2)) / 4
C4  = 0.291004656460458948525731457501  = (16 * sqrt(2) - 9 * sqrt(6)) / 2
C5  = 0.427799838583676096484617883106  = sqrt(sqrt(3) - 1) / 2
C6  = 0.517638090205041524697797675248  = (sqrt(6) - sqrt(2)) / 2
C7  = 0.7071067811865475244008443621048 = sqrt(2) / 2
C8  = 0.795039506689100575281206278317  = (7 * sqrt(6) - 11 * sqrt(2)) / 2
C9  = 0.965925826289068286749743199729  = (sqrt(2) + sqrt(6)) / 4
C10 = 1.08604416314955952380693773582   = (5 * sqrt(2) - 2 * sqrt(6)) / 2

V0  = (  C9,  -C3,  C5)
V1  = (  C9,   C3, -C5)
V2  = ( -C9,   C3,  C5)
V3  = ( -C9,  -C3, -C5)
V4  = (  C3,  -C9,  C5)
V5  = (  C3,   C9, -C5)
V6  = ( -C3,   C9,  C5)
V7  = ( -C3,  -C9, -C5)
V8  = (  C7,   C7,  C5)
V9  = (  C7,  -C7, -C5)
V10 = ( -C7,  -C7,  C5)
V11 = ( -C7,   C7, -C5)
V12 = ( C10,  -C4,  C1)
V13 = ( C10,   C4, -C1)
V14 = (-C10,   C4,  C1)
V15 = (-C10,  -C4, -C1)
V16 = (  C4, -C10,  C1)
V17 = (  C4,  C10, -C1)
V18 = ( -C4,  C10,  C1)
V19 = ( -C4, -C10, -C1)
V20 = (  C8,   C8,  C1)
V21 = (  C8,  -C8, -C1)
V22 = ( -C8,  -C8,  C1)
V23 = ( -C8,   C8, -C1)
V24 = (  C7,   C2,  C0)
V25 = (  C7,  -C2, -C0)
V26 = ( -C7,  -C2,  C0)
V27 = ( -C7,   C2, -C0)
V28 = (  C2,   C7,  C0)
V29 = (  C2,  -C7, -C0)
V30 = ( -C2,  -C7,  C0)
V31 = ( -C2,   C7, -C0)
V32 = (  C6,  -C6,  C0)
V33 = (  C6,   C6, -C0)
V34 = ( -C6,   C6,  C0)
V35 = ( -C6,  -C6, -C0)

Faces:
{  0,  4, 16, 21, 12 }
{  0, 12, 13, 20,  8 }
{  0,  8, 33, 24, 25 }
{  0, 25, 32, 29,  4 }
{  1,  5, 17, 20, 13 }
{  1, 13, 12, 21,  9 }
{  1,  9, 32, 25, 24 }
{  1, 24, 33, 28,  5 }
{  6,  2, 27, 34, 31 }
{  6, 31, 28, 33,  8 }
{  6,  8, 20, 17, 18 }
{  6, 18, 23, 14,  2 }
{  7,  3, 26, 35, 30 }
{  7, 30, 29, 32,  9 }
{  7,  9, 21, 16, 19 }
{  7, 19, 22, 15,  3 }
{ 10,  2, 14, 15, 22 }
{ 10, 22, 19, 16,  4 }
{ 10,  4, 29, 30, 35 }
{ 10, 35, 26, 27,  2 }
{ 11,  3, 15, 14, 23 }
{ 11, 23, 18, 17,  5 }
{ 11,  5, 28, 31, 34 }
{ 11, 34, 27, 26,  3 }