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
3x3U .F . U. o5U
4F3F .Z . F. x5F
5Z3x .U . Z. F5x
6U3F .A . x. U5o
7aF3U .F . A. F5o
7bB . o
8x3Z .x . B. x5x
opposite {10}
9aF3F .F . A 
9bB . o
10U3x .A . x
11F3o .U . Z
12x3o .
opposite {3}
Z . F
13 F . U
14x . F
15o . x
opposite edge
(F=ff, U=uf, Z=fff, A=ff.x(10), B=ff.sqrt(5))
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°
Confer
Grünbaumian relatives:
2tid  
variations:
a3b5c   o3(-x)5f  
related Johnson solids:
autid   pabautid   mabautid   tautid  
External
links
hedrondude   wikipedia   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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