Acronym tic
TOCID symbol tC
Name truncated cube,
truncated hexahedron

` © ©`
Circumradius sqrt[7+4 sqrt(2)]/2 = 1.778824
Inradius
wrt. {8}
[1+sqrt(2)]/2 = 1.207107
Inradius
wrt. {3}
(3+2 sqrt(2))/sqrt(12) = 1.682522
Vertex figure [3,82] = xo&#x(8,2)
Vertex layers
 Layer Symmetry Subsymmetries o3o4o o3o . o . o . o4o 1 o3x4x o3x .{3} first o . xedge first . x4x{8} first 2 o3w . x . w . o4w 3 x3w . w . w . o4w 4 w3x . W . x . x4xopposite {8} 5 w3o . w . w 6 x3o .opposite {3} x . w 7 o . xopposite 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
Volume (21+14 sqrt(2))/3 = 13.599663
Surface 12+12 sqrt(2)+2 sqrt(3) = 32.434664
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
analogs:
truncated hypercube tCn
External
links

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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