Acronym tid
TOCID symbol tD
Name truncated dodecahedron
 
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Circumradius sqrt[(37+15 sqrt(5))/8] = 2.969449
Vertex figure [3,102]
Vertex layers
LayerSymmetrySubsymmetries
 o3o5oo3o .o . o. o5o
1o3x5xo3x .
{3} first
o . x
edge first
. x5x
{10} first
2o3F .x . F. o5F
3x3V .F . V. o5V
4F3F .B . F. x5F
5aB3x .V . B. F5x
5bC . x
6aV3F .F . C. V5o
6bD . o
7F3V .x . D. F5o
8ax3B .F . C. x5x
opposite {10}
8bD . o
9aF3F .V . B 
9bC . x
10V3x .B . F
11F3o .F . V
12x3o .
opposite {3}
x . F
13 o . x
opposite edge
(F = ff = f+x, V = uf = 2f, B = fff = 2f+x, C = uff = 2f+2x, D = ff.sqrt(5) = 3f+x)
General of army (is itself convex)
Colonel of regiment (is itself locally convex – no other uniform polyhedral members)
Dihedral angles
  • between {3} and {10}:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
  • between {10} and {10}:   arccos(-1/sqrt(5)) = 116.565051°
Face vector 60, 90, 32
Confer
Grünbaumian relatives:
2tid  
variations:
a3b5c   o3(-x)5f  
related Johnson solids:
autid   pabautid   mabautid   tautid  
ambification:
retid  
general polytopal classes:
Wythoffian polyhedra  
External
links
hedrondude   wikipedia   polytopewiki   WikiChoron   mathworld   quickfur

As abstract polytope tid is isomorphic to quit gissid, thereby replacing decagons by decagrams.


Incidence matrix according to Dynkin symbol

o3x5x

. . . | 60 |  2  1 |  1  2
------+----+-------+------
. x . |  2 | 60  * |  1  1
. . x |  2 |  * 30 |  0  2
------+----+-------+------
o3x . |  3 |  3  0 | 20  *
. x5x | 10 |  5  5 |  * 12

snubbed forms: o3β5x, o3x5β, o3β5β

o3/2x5x

.   . . | 60 |  2  1 |  1  2
--------+----+-------+------
.   x . |  2 | 60  * |  1  1
.   . x |  2 |  * 30 |  0  2
--------+----+-------+------
o3/2x . |  3 |  3  0 | 20  *
.   x5x | 10 |  5  5 |  * 12

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