Acronym tic
TOCID symbol tC
Name truncated cube,
truncated hexahedron
 
 © ©
Circumradius sqrt[7+4 sqrt(2)]/2 = 1.778824
Vertex figure [3,82] = xo&#x(8,2)
Vertex layers
LayerSymmetrySubsymmetries
 o3o4oo3o .o . o. o4o
1o3x4xo3x .
{3} first
o . x
edge first
. x4x
{8} first
2o3w .x . w. o4w
3x3w .w . w. o4w
4w3x .W . x. x4x
opposite {8}
5w3o .w . w 
6x3o .
opposite {3}
x . w
7 o . x
opposite edge
Lace city
in approx. ASCII-art
x w   w x
w       w
         
w       w
x w   w x
  x w   w x  
o     U     o	(U=qw=u+q=x+w)
             
o     U     o
  x w   w x  
Coordinates ((1+sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – no other uniform polyhedral members)
Dihedral angles
  • between {3} and {8}:   arccos(-1/sqrt(3)) = 125.264390°
  • between {8} and {8}:   90°
Dual tikko
Confer
Grünbaumian relatives:
2tic  
related Johnson solids:
autic   bautic  
variations:
a3b4c   o3x4q   o3x4u   o3q4x  
decompositions:
cube || tic  
blends:
tutic  
compounds:
tar  
unit-edged relatives:
mono-lower-tic   para-bi-lower-tic   pactic  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia   WikiChoron   mathworld   quickfur

As abstract polytope tic is isomorphic to quith, thereby replacing octagons by octagrams.

Note that tic can be thought of as the external blend of 1 cube + 8 tets + 6 squacues, cf. the Steward toroid T4 \ Q4P4Q4. This decomposition is also described as the degenerate segmentochoron oo3ox4xx&#xt.


Incidence matrix according to Dynkin symbol

o3x4x

. . . | 24 |  2  1 | 1 2
------+----+-------+----
. x . |  2 | 24  * | 1 1
. . x |  2 |  * 12 | 0 2
------+----+-------+----
o3x . |  3 |  3  0 | 8 *
. x4x |  8 |  4  4 | * 6

snubbed forms: o3β4x, o3x4s, o3β4β

o3/2x4x

.   . . | 24 |  2  1 | 1 2
--------+----+-------+----
.   x . |  2 | 24  * | 1 1
.   . x |  2 |  * 12 | 0 2
--------+----+-------+----
o3/2x . |  3 |  3  0 | 8 *
.   x4x |  8 |  4  4 | * 6

xwwx4xoox&#xt   → outer heights = 1/sqrt(2) = 0.707107
                   inner height = 1
({8} || pseudo w-{4} || pseudo w-{4} || {8})

o...4o...     | 8 * * * | 1 1 1 0 0 0 0 | 1 1 1 0 0
.o..4.o..     | * 4 * * | 0 0 2 1 0 0 0 | 0 1 2 0 0
..o.4..o.     | * * 4 * | 0 0 0 1 2 0 0 | 0 0 2 1 0
...o4...o     | * * * 8 | 0 0 0 0 1 1 1 | 0 0 1 1 1
--------------+---------+---------------+----------
x... ....     | 2 0 0 0 | 4 * * * * * * | 1 0 1 0 0
.... x...     | 2 0 0 0 | * 4 * * * * * | 1 1 0 0 0
oo..4oo..&#x  | 1 1 0 0 | * * 8 * * * * | 0 1 1 0 0
.oo.4.oo.&#x  | 0 1 1 0 | * * * 4 * * * | 0 0 2 0 0
..oo4..oo&#x  | 0 0 1 1 | * * * * 8 * * | 0 0 1 1 0
...x ....     | 0 0 0 2 | * * * * * 4 * | 0 0 1 0 1
.... ...x     | 0 0 0 2 | * * * * * * 4 | 0 0 0 1 1
--------------+---------+---------------+----------
x...4x...     | 8 0 0 0 | 4 4 0 0 0 0 0 | 1 * * * *
.... xo..&#x  | 2 1 0 0 | 0 1 2 0 0 0 0 | * 4 * * *
xwwx ....&#xt | 2 2 2 2 | 1 0 2 2 2 1 0 | * * 4 * *
.... ..ox&#x  | 0 0 1 2 | 0 0 0 0 2 0 1 | * * * 4 *
...x4...x     | 0 0 0 8 | 0 0 0 0 0 4 4 | * * * * 1
or
o...4o...      & | 16 * | 1 1  1 0 | 1 1 1
.o..4.o..      & |  * 8 | 0 0  2 1 | 0 1 2
-----------------+------+----------+------
x... ....      & |  2 0 | 8 *  * * | 1 0 1
.... x...      & |  2 0 | * 8  * * | 1 1 0
oo..4oo..&#x   & |  1 1 | * * 16 * | 0 1 1
.oo.4.oo.&#x     |  0 2 | * *  * 4 | 0 0 2
-----------------+------+----------+------
x...4x...      & |  8 0 | 4 4  0 0 | 2 * *
.... xo..&#x   & |  2 1 | 0 1  2 0 | * 8 *
xwwx ....&#xt    |  4 4 | 2 0  4 2 | * * 4

xwwxoo3ooxwwx&#xt   → height(1,2) = height(3,4) = height(5,6) = 1/sqrt(3) = 0.577350
                       height(2,3) = height(4,5) = sqrt(2/3) = 0.816497
({3} || pseudo w-{3} || pseudo (w,x)-{6} || pseudo (x,w)-{6} || pseudo dual w-{3} || dual {3})

o.....3o.....     | 3 * * * * * | 2 1 0 0 0 0 0 0 0 | 1 2 0 0 0 0
.o....3.o....     | * 3 * * * * | 0 1 2 0 0 0 0 0 0 | 0 2 1 0 0 0
..o...3..o...     | * * 6 * * * | 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 0
...o..3...o..     | * * * 6 * * | 0 0 0 0 1 1 1 0 0 | 0 1 0 1 1 0
....o.3....o.     | * * * * 3 * | 0 0 0 0 0 0 2 1 0 | 0 0 0 2 1 0
.....o3.....o     | * * * * * 3 | 0 0 0 0 0 0 0 1 2 | 0 0 0 2 0 1
------------------+-------------+-------------------+------------
x..... ......     | 2 0 0 0 0 0 | 3 * * * * * * * * | 1 1 0 0 0 0
oo....3oo....&#x  | 1 1 0 0 0 0 | * 3 * * * * * * * | 0 2 0 0 0 0
.oo...3.oo...&#x  | 0 1 1 0 0 0 | * * 6 * * * * * * | 0 1 1 0 0 0
...... ..x...     | 0 0 2 0 0 0 | * * * 3 * * * * * | 0 0 1 1 0 0
..oo..3..oo..&#x  | 0 0 1 1 0 0 | * * * * 6 * * * * | 0 1 0 1 0 0
...x.. ......     | 0 0 0 2 0 0 | * * * * * 3 * * * | 0 1 0 0 1 0
...oo.3...oo.&#x  | 0 0 0 1 1 0 | * * * * * * 6 * * | 0 0 0 1 1 0
....oo3....oo&#x  | 0 0 0 0 1 1 | * * * * * * * 3 * | 0 0 0 2 0 0
...... .....x     | 0 0 0 0 0 2 | * * * * * * * * 3 | 0 0 0 1 0 1
------------------+-------------+-------------------+------------
x.....3o.....     | 3 0 0 0 0 0 | 3 0 0 0 0 0 0 0 0 | 1 * * * * *
xwwx.. ......&#xt | 2 2 2 2 0 0 | 1 2 2 0 2 1 0 0 0 | * 3 * * * *
...... .ox...&#x  | 0 1 2 0 0 0 | 0 0 2 1 0 0 0 0 0 | * * 3 * * *
...... ..xwwx&#xt | 0 0 2 2 2 2 | 0 0 0 1 2 0 2 2 1 | * * * 3 * *
...xo. ......&#x  | 0 0 0 2 1 0 | 0 0 0 0 0 1 2 0 0 | * * * * 3 *
.....o3.....x     | 0 0 0 0 0 3 | 0 0 0 0 0 0 0 0 3 | * * * * * 1
or
o.....3o.....      & | 6 *  * | 2 1  0 0 0 | 1 2 0
.o....3.o....      & | * 6  * | 0 1  2 0 0 | 0 2 1
..o...3..o...      & | * * 12 | 0 0  1 1 1 | 0 2 1
---------------------+--------+------------+------
x..... ......      & | 2 0  0 | 6 *  * * * | 1 1 0
oo....3oo....&#x   & | 1 1  0 | * 6  * * * | 0 2 0
.oo...3.oo...&#x   & | 0 1  1 | * * 12 * * | 0 1 1
...... ..x...      & | 0 0  2 | * *  * 6 * | 0 1 1
..oo..3..oo..&#x     | 0 0  2 | * *  * * 6 | 0 2 0
---------------------+--------+------------+------
x.....3o.....      & | 3 0  0 | 3 0  0 0 0 | 2 * *
xwwx.. ......&#xt  & | 2 2  4 | 1 2  2 1 2 | * 6 *
...... .ox...&#x   & | 0 1  2 | 0 0  2 1 0 | * * 6

wx3oo3xw&#zx   → height = 0
(tegum sum of 2 mutually inverted (x,w)-coes)

o.3o.3o.     | 12  * |  2  1  0 | 1 2 0
.o3.o3.o     |  * 12 |  0  1  2 | 0 2 1
-------------+-------+----------+------
.. .. x.     |  2  0 | 12  *  * | 1 1 0
oo3oo3oo&#x  |  1  1 |  * 12  * | 0 2 0
.x .. ..     |  0  2 |  *  * 12 | 0 1 1
-------------+-------+----------+------
.. o.3x.     |  3  0 |  3  0  0 | 4 * *
wx .. xw&#zx |  4  4 |  2  4  2 | * 6 *
.x3.o ..     |  0  3 |  0  0  3 | * * 4
or
o.3o.3o.     & | 24 |  2  1 | 1 2
---------------+----+-------+----
.. .. x.     & |  2 | 24  * | 1 1
oo3oo3oo&#x    |  2 |  * 12 | 0 2
---------------+----+-------+----
.. o.3x.     & |  3 |  3  0 | 8 *
wx .. xw&#zx   |  8 |  4  4 | * 6

wx xw4xo&#zx   → height = 0
(tegum sum of (w,x,x)-op and (x,w,w)-cube)

o. o.4o.     | 16 * | 1 1  1 0 | 1 1 1
.o .o4.o     |  * 8 | 0 0  2 1 | 0 2 1
-------------+------+----------+------
.. x. ..     |  2 0 | 8 *  * * | 1 1 0
.. .. x.     |  2 0 | * 8  * * | 1 0 1
oo oo4oo&#x  |  1 1 | * * 16 * | 0 1 1
.x .. ..     |  0 2 | * *  * 4 | 0 2 0
-------------+------+----------+------
.. x.4x.     |  8 0 | 4 4  0 0 | 2 * *
wx xw ..&#zx |  4 4 | 2 0  4 2 | * 4 *
.. .. xo&#x  |  2 1 | 0 1  2 0 | * * 8

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