Acronym	tutatoe, tut || toe, K-4.76
Name	truncated tetrahedron atop truncated octahedron, truncated-tetrahedral cap of prismatorhombated pentachoron, tetrahedral canticupola
Segmentochoron display / VRML	⭳
Circumradius	sqrt(13/5) = 1.612452
Lace city in approx. ASCII-art	o3x o3u x3x -- o3x3x (tut) x3x x3u u3x x3x -- x3x3x (toe)
	o x x u u x x o -- o3x3x (tut) x x u u xw wx u u x x -- x3x3x (toe)
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	at {4} between hip and trip:   arccos(-2/3) = 131.810315° at {6} between hip and tut:   arccos[-sqrt(3/8)] = 127.761244° at {3} between tricu and trip:   arccos[-sqrt(3/8)] = 127.761244° at {4} between hip and tricu:   arccos[-1/sqrt(6)] = 114.094843° at {3} between tricu and tut:   arccos(-1/4) = 104.477512° at {6} between toe and tricu:   arccos(1/4) = 75.522488° at {4} between toe and trip:   arccos(sqrt[1/6]) = 65.905157° at {6} between hip and toe:   arccos(sqrt[3/8]) = 52.238756°
Face vector	36, 78, 58, 16
Confer	uniform relative: prip   related CRFs: tutatobcu   tutatoe gybcu   etutatoe   tutatoe augrip   tutatoa sirco   general polytopal classes: segmentochora   lace simplices
External links

Incidence matrix according to Dynkin symbol

xx3xx3ox&#x   → height = sqrt(5/8) = 0.790569
(tut || toe)

o.3o.3o.    | 12  * | 1  2  2  0  0  0 | 2 1  2  2  1 0 0 0 | 1 2 1 1 0
.o3.o3.o    |  * 24 | 0  0  1  1  1  1 | 0 0  1  1  1 1 1 1 | 0 1 1 1 1
------------+-------+------------------+--------------------+----------
x. .. ..    |  2  0 | 6  *  *  *  *  * | 2 0  2  0  0 0 0 0 | 1 2 1 0 0
.. x. ..    |  2  0 | * 12  *  *  *  * | 1 1  0  1  0 0 0 0 | 1 1 0 1 0
oo3oo3oo&#x |  1  1 | *  * 24  *  *  * | 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.x .. ..    |  0  2 | *  *  * 12  *  * | 0 0  1  0  0 1 1 0 | 0 1 1 0 1
.. .x ..    |  0  2 | *  *  *  * 12  * | 0 0  0  1  0 1 0 1 | 0 1 0 1 1
.. .. .x    |  0  2 | *  *  *  *  * 12 | 0 0  0  0  1 0 1 1 | 0 0 1 1 1
------------+-------+------------------+--------------------+----------
x.3x. ..    |  6  0 | 3  3  0  0  0  0 | 4 *  *  *  * * * * | 1 1 0 0 0
.. x.3o.    |  3  0 | 0  3  0  0  0  0 | * 4  *  *  * * * * | 1 0 0 1 0
xx .. ..&#x |  2  2 | 1  0  2  1  0  0 | * * 12  *  * * * * | 0 1 1 0 0
.. xx ..&#x |  2  2 | 0  1  2  0  1  0 | * *  * 12  * * * * | 0 1 0 1 0
.. .. ox&#x |  1  2 | 0  0  2  0  0  1 | * *  *  * 12 * * * | 0 0 1 1 0
.x3.x ..    |  0  6 | 0  0  0  3  3  0 | * *  *  *  * 4 * * | 0 1 0 0 1
.x .. .x    |  0  4 | 0  0  0  2  0  2 | * *  *  *  * * 6 * | 0 0 1 0 1
.. .x3.x    |  0  6 | 0  0  0  0  3  3 | * *  *  *  * * * 4 | 0 0 0 1 1
------------+-------+------------------+--------------------+----------
x.3x.3o.    ♦ 12  0 | 6 12  0  0  0  0 | 4 4  0  0  0 0 0 0 | 1 * * * *
xx3xx ..&#x ♦  6  6 | 3  3  6  3  3  0 | 1 0  3  3  0 1 0 0 | * 4 * * *
xx .. ox&#x ♦  2  4 | 1  0  4  2  0  2 | 0 0  2  0  2 0 1 0 | * * 6 * *
.. xx3ox&#x ♦  3  6 | 0  3  6  0  3  3 | 0 1  0  3  3 0 0 1 | * * * 4 *
.x3.x3.x    ♦  0 24 | 0  0  0 12 12 12 | 0 0  0  0  0 4 6 4 | * * * * 1

xx3ox4so&#x   → height = sqrt(5/8) = 0.790569
(tut || toe)

demi( o.3o.4o.    ) | 12  * |  2 1  2  0  0  0 | 1 2  2  1  2 0 0 0 | 1 1 1 2 0
      .o3.o4.o      |  * 24 |  0 0  1  1  1  1 | 0 0  1  1  1 1 1 1 | 0 1 1 1 1
--------------------+-------+------------------+--------------------+----------
demi( x. .. ..    ) |  2  0 | 12 *  *  *  *  * | 1 1  1  0  0 0 0 0 | 1 1 0 1 0
      .. o.4s.      |  2  0 |  * 6  *  *  *  * | 0 2  0  0  2 0 0 0 | 1 0 1 2 0
demi( oo3oo4oo&#x ) |  1  1 |  * * 24  *  *  * | 0 0  1  1  1 0 0 0 | 0 1 1 1 0
      .x .. ..      |  0  2 |  * *  * 12  *  * | 0 0  1  0  0 1 1 0 | 0 1 0 1 1
demi( .. .x ..    ) |  0  2 |  * *  *  * 12  * | 0 0  0  0  1 1 0 1 | 0 0 1 1 1
demi( .. .x ..    ) |  0  2 |  * *  *  *  * 12 | 0 0  0  1  0 0 1 1 | 0 1 1 0 1
--------------------+-------+------------------+--------------------+----------
demi( x.3o. ..    ) |  3  0 |  3 0  0  0  0  0 | 4 *  *  *  * * * * | 1 1 0 0 0
sefa( x.3o.4s.    ) |  6  0 |  3 3  0  0  0  0 | * 4  *  *  * * * * | 1 0 0 1 0
demi( xx .. ..&#x ) |  2  2 |  1 0  2  1  0  0 | * * 12  *  * * * * | 0 1 0 1 0
demi( .. ox ..&#x ) |  1  2 |  0 0  2  0  0  1 | * *  * 12  * * * * | 0 1 1 0 0
sefa( .. ox4so&#x ) |  2  2 |  0 1  2  0  1  0 | * *  *  * 12 * * * | 0 0 1 1 0
demi( .x3.x ..    ) |  0  6 |  0 0  0  3  3  0 | * *  *  *  * 4 * * | 0 0 0 1 1
demi( .x3.x ..    ) |  0  6 |  0 0  0  3  0  3 | * *  *  *  * * 4 * | 0 1 0 0 1
      .. .x4.o      |  0  4 |  0 0  0  0  2  2 | * *  *  *  * * * 6 | 0 0 1 0 1
--------------------+-------+------------------+--------------------+----------
      x.3o.4s.      ♦ 12  0 | 12 6  0  0  0  0 | 4 4  0  0  0 0 0 0 | 1 * * * *
demi( xx3ox ..&#x ) ♦  3  6 |  3 0  6  3  0  3 | 1 0  3  3  0 0 1 0 | * 4 * * *
      .. ox4so&#x   ♦  2  4 |  0 1  4  0  2  2 | 0 0  0  2  2 0 0 1 | * * 6 * *
sefa( xx3ox4so&#x ) ♦  6  6 |  3 3  6  3  3  0 | 0 1  3  0  3 1 0 0 | * * * 4 *
      .x3.x4.o      ♦  0 24 |  0 0  0 12 12 12 | 0 0  0  0  0 4 4 6 | * * * * 1

starting figure: xx3ox4xo&#x