Acronym tutatoa sirco
Name truncated tetrahedron atop truncated octahedron atop small rhombicuboctahedron
Circumradius ...
Dihedral angles
(at margins)
  • at {3} between tricu and tricu (across rim):   arccos[-(3-sqrt(8)+sqrt[90 sqrt(8)-135])/sqrt(128)] = 169.000195°
  • at {3} between hip and tricu (across rim):   arccos[-(3-sqrt(8)+sqrt[30 sqrt(8)-45])/sqrt(48)] = 159.382864°
  • at {4} between squap and trip (across rim):   arccos[-(1-sqrt(2)+sqrt[20 sqrt(2)-15])/sqrt(12 sqrt(2))] = 141.646907°
  • at {4} between tricu and trip (in sircoatoe):   arccos[-(sqrt(8)-1)/sqrt(6)] = 138.283988°
  • at {3} between squap and trip (in sircoatoe):   arccos[-sqrt(3 sqrt(2)/8)] = 136.738853°
  • at {4} between hip and trip (in tutatoe):   arccos(-2/3) = 131.810315°
  • at {6} between hip and tut (in tutatoe):   arccos[-sqrt(3/8)] = 127.761244°
  • at {3} between squap and tricu (in sircoatoe):   arccos[-(sqrt(8)-1)/sqrt(sqrt(128))] = 122.928678°
  • at {4} between sirco and trip (in sircoatoe):   arccos[-(2-sqrt(2))/sqrt(3)] = 109.767487°
  • at {4} between sirco and squap (in sircoatoe):   arccos[-(sqrt(2)-1)/sqrt(sqrt(8))] = 104.258250°
  • at {3} between sirco and tricu (in sircoatoe):   arccos[(3-sqrt(8))/sqrt(8)] = 86.522293°
Face vector 60, 174, 158, 42
Confer
related segmentochora:
sirco || toe   tut || toe  
general polytopal classes:
bistratic lace towers  

Incidence matrix according to Dynkin symbol

xx(oq)3xx(xx)3ox(qo)&#xt   → height(1,2) = sqrt(5/8) = 0.790569
                             height(2,3) = sqrt[sqrt(2)-3/4] = 0.814993
(tut || toe || sirco)

o.(..)3o.(..)3o.(..)     | 12  *  *  * | 1  2  2  0  0  0  0  0  0  0  0 | 2 1  2  2  1 0 0 0  0  0  0  0  0 0 0  0 0 | 1 2 1 1 0 0 0  0 0
.o(..)3.o(..)3.o(..)     |  * 24  *  * | 0  0  1  1  1  1  1  1  0  0  0 | 0 0  1  1  1 1 1 1  1  1  1  1  1 0 0  0 0 | 0 1 1 1 1 1 1  1 0
..(o.)3..(o.)3..(o.)     |  *  * 12  * | 0  0  0  0  0  0  2  0  2  2  0 | 0 0  0  0  0 0 0 0  1  2  2  0  0 1 1  2 0 | 0 0 0 0 1 0 1  2 1
..(.o)3..(.o)3..(.o)     |  *  *  * 12 | 0  0  0  0  0  0  0  2  0  2  2 | 0 0  0  0  0 0 0 0  0  0  2  2  1 0 1  2 1 | 0 0 0 0 0 1 1  2 1
-------------------------+-------------+---------------------------------+--------------------------------------------+-------------------
x.(..) ..(..) ..(..)     |  2  0  0  0 | 6  *  *  *  *  *  *  *  *  *  * | 2 0  2  0  0 0 0 0  0  0  0  0  0 0 0  0 0 | 1 2 1 0 0 0 0  0 0
..(..) x.(..) ..(..)     |  2  0  0  0 | * 12  *  *  *  *  *  *  *  *  * | 1 1  0  1  0 0 0 0  0  0  0  0  0 0 0  0 0 | 1 1 0 1 0 0 0  0 0
oo(..)3oo(..)3oo(..)&#x  |  1  1  0  0 | *  * 24  *  *  *  *  *  *  *  * | 0 0  1  1  1 0 0 0  0  0  0  0  0 0 0  0 0 | 0 1 1 1 0 0 0  0 0
.x(..) ..(..) ..(..)     |  0  2  0  0 | *  *  * 12  *  *  *  *  *  *  * | 0 0  1  0  0 1 1 0  1  0  0  0  0 0 0  0 0 | 0 1 1 0 1 0 1  0 0
..(..) .x(..) ..(..)     |  0  2  0  0 | *  *  *  * 12  *  *  *  *  *  * | 0 0  0  1  0 1 0 1  0  1  0  1  0 0 0  0 0 | 0 1 0 1 1 1 0  1 0
..(..) ..(..) .x(..)     |  0  2  0  0 | *  *  *  *  * 12  *  *  *  *  * | 0 0  0  0  1 0 1 1  0  0  0  0  1 0 0  0 0 | 0 0 1 1 0 1 1  0 0
.o(o.)3.o(o.)3.o(o.)&#x  |  0  1  1  0 | *  *  *  *  *  * 24  *  *  *  * | 0 0  0  0  0 0 0 0  1  1  1  0  0 0 0  0 0 | 0 0 0 0 1 0 1  1 0
.o(.o)3.o(.o)3.o(.o)&#x  |  0  1  0  1 | *  *  *  *  *  *  * 24  *  *  * | 0 0  0  0  0 0 0 0  0  0  1  1  1 0 0  0 0 | 0 0 0 0 0 1 1  1 0
..(..) ..(x.) ..(..)     |  0  0  2  0 | *  *  *  *  *  *  *  * 12  *  * | 0 0  0  0  0 0 0 0  0  1  0  0  0 1 0  1 0 | 0 0 0 0 1 0 0  1 1
..(oo)3..(oo)3..(oo)&#x  |  0  0  1  1 | *  *  *  *  *  *  *  *  * 24  * | 0 0  0  0  0 0 0 0  0  0  1  0  0 0 1  1 0 | 0 0 0 0 0 0 1  1 1
..(..) ..(.x) ..(..)     |  0  0  0  2 | *  *  *  *  *  *  *  *  *  * 12 | 0 0  0  0  0 0 0 0  0  0  0  1  0 0 0  1 1 | 0 0 0 0 0 1 0  1 1
-------------------------+-------------+---------------------------------+--------------------------------------------+-------------------
x.(..)3x.(..) ..(..)     |  6  0  0  0 | 3  3  0  0  0  0  0  0  0  0  0 | 4 *  *  *  * * * *  *  *  *  *  * * *  * * | 1 1 0 0 0 0 0  0 0
..(..) x.(..)3o.(..)     |  3  0  0  0 | 0  3  0  0  0  0  0  0  0  0  0 | * 4  *  *  * * * *  *  *  *  *  * * *  * * | 1 0 0 1 0 0 0  0 0
xx(..) ..(..) ..(..)&#x  |  2  2  0  0 | 1  0  2  1  0  0  0  0  0  0  0 | * * 12  *  * * * *  *  *  *  *  * * *  * * | 0 1 1 0 0 0 0  0 0
..(..) xx(..) ..(..)&#x  |  2  2  0  0 | 0  1  2  0  1  0  0  0  0  0  0 | * *  * 12  * * * *  *  *  *  *  * * *  * * | 0 1 0 1 0 0 0  0 0
..(..) ..(..) ox(..)&#x  |  1  2  0  0 | 0  0  2  0  0  1  0  0  0  0  0 | * *  *  * 12 * * *  *  *  *  *  * * *  * * | 0 0 1 1 0 0 0  0 0
.x(..)3.x(..) ..(..)     |  0  6  0  0 | 0  0  0  3  3  0  0  0  0  0  0 | * *  *  *  * 4 * *  *  *  *  *  * * *  * * | 0 1 0 0 1 0 0  0 0
.x(..) ..(..) .x(..)     |  0  4  0  0 | 0  0  0  2  0  2  0  0  0  0  0 | * *  *  *  * * 6 *  *  *  *  *  * * *  * * | 0 0 1 0 0 0 1  0 0
..(..) .x(..)3.x(..)     |  0  6  0  0 | 0  0  0  0  3  3  0  0  0  0  0 | * *  *  *  * * * 4  *  *  *  *  * * *  * * | 0 0 0 1 0 1 0  0 0
.x(o.) ..(..) ..(..)&#x  |  0  2  1  0 | 0  0  0  1  0  0  2  0  0  0  0 | * *  *  *  * * * * 12  *  *  *  * * *  * * | 0 0 0 0 1 0 1  0 0
..(..) .x(x.) ..(..)&#x  |  0  2  2  0 | 0  0  0  0  1  0  2  0  1  0  0 | * *  *  *  * * * *  * 12  *  *  * * *  * * | 0 0 0 0 1 0 0  1 0
.o(oo)3.o(oo)3.o(oo)&#x  |  0  1  1  1 | 0  0  0  0  0  0  1  1  0  1  0 | * *  *  *  * * * *  *  * 24  *  * * *  * * | 0 0 0 0 0 0 1  1 0
..(..) .x(.x) ..(..)&#x  |  0  2  0  2 | 0  0  0  0  1  0  0  2  0  0  1 | * *  *  *  * * * *  *  *  * 12  * * *  * * | 0 0 0 0 0 1 0  1 0
..(..) ..(..) .x(.o)&#x  |  0  2  0  1 | 0  0  0  0  0  1  0  2  0  0  0 | * *  *  *  * * * *  *  *  *  * 12 * *  * * | 0 0 0 0 0 1 1  0 0
..(o.)3..(x.) ..(..)     |  0  0  3  0 | 0  0  0  0  0  0  0  0  3  0  0 | * *  *  *  * * * *  *  *  *  *  * 4 *  * * | 0 0 0 0 1 0 0  0 1
..(oq) ..(..) ..(qo)&#zx |  0  0  2  2 | 0  0  0  0  0  0  0  0  0  4  0 | * *  *  *  * * * *  *  *  *  *  * * 6  * * | 0 0 0 0 0 0 1  0 1
..(..) ..(xx) ..(..)&#x  |  0  0  2  2 | 0  0  0  0  0  0  0  0  1  2  1 | * *  *  *  * * * *  *  *  *  *  * * * 12 * | 0 0 0 0 0 0 0  1 1
..(..) ..(.x)3..(.o)     |  0  0  0  3 | 0  0  0  0  0  0  0  0  0  0  3 | * *  *  *  * * * *  *  *  *  *  * * *  * 4 | 0 0 0 0 0 1 0  0 1
-------------------------+-------------+---------------------------------+--------------------------------------------+-------------------
x.(..)3x.(..)3o.(..)     ♦ 12  0  0  0 | 6 12  0  0  0  0  0  0  0  0  0 | 4 4  0  0  0 0 0 0  0  0  0  0  0 0 0  0 0 | 1 * * * * * *  * *
xx(..)3xx(..) ..(..)&#x  ♦  6  6  0  0 | 3  3  6  3  3  0  0  0  0  0  0 | 1 0  3  3  0 1 0 0  0  0  0  0  0 0 0  0 0 | * 4 * * * * *  * *
xx(..) ..(..) ox(..)&#x  ♦  2  4  0  0 | 1  0  4  2  0  2  0  0  0  0  0 | 0 0  2  0  2 0 1 0  0  0  0  0  0 0 0  0 0 | * * 6 * * * *  * *
..(..) xx(..)3ox(..)&#x  ♦  3  6  0  0 | 0  3  6  0  3  3  0  0  0  0  0 | 0 1  0  3  3 0 0 1  0  0  0  0  0 0 0  0 0 | * * * 4 * * *  * *
.x(o.)3.x(x.) ..(..)&#x  ♦  0  6  3  0 | 0  0  0  3  3  0  6  0  3  0  0 | 0 0  0  0  0 1 0 0  3  3  0  0  0 1 0  0 0 | * * * * 4 * *  * *
..(..) .x(.x)3.x(.o)&#x  ♦  0  6  0  3 | 0  0  0  0  3  3  0  6  0  0  3 | 0 0  0  0  0 0 0 1  0  0  0  3  3 0 0  0 1 | * * * * * 4 *  * *
.x(oq) ..(..) .x(qo)&#x  ♦  0  4  2  2 | 0  0  0  2  0  2  4  4  0  4  0 | 0 0  0  0  0 0 1 0  2  0  4  0  2 0 1  0 0 | * * * * * * 6  * *
..(..) .x(xx) ..(..)&#x  ♦  0  2  2  2 | 0  0  0  0  1  0  2  2  1  2  1 | 0 0  0  0  0 0 0 0  0  1  2  1  0 0 0  1 0 | * * * * * * * 12 *
..(oq)3..(xx)3..(qo)&#zx ♦  0  0 12 12 | 0  0  0  0  0  0  0  0 12 24 12 | 0 0  0  0  0 0 0 0  0  0  0  0  0 4 6 12 4 | * * * * * * *  * 1

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