Acronym	tetaco, tet || co, K-4.23
Name	tetrahedron atop cuboctahedron, tetrahedral rotunda of small prismatodecachoron
Segmentochoron display / VRML	⭳
Circumradius	1
Lace city in approx. ASCII-art	x3o o3o -- x3o3o (tet) x3o x3x o3x -- x3o3x (co)
	x o o x -- x3o3o (tet) x x ou uo x x -- x3o3x (co)
Volume	35 sqrt(5)/96 = 0.815233
Dihedral angles	at {4} between trip and trip:   arccos(-2/3) = 131.810315° at {3} between tet and trip:   arccos(-sqrt(3/8)) = 127.761244° at {3} between co and tet:   arccos(1/4) = 75.522488° at {4} between co and trip:   arccos(sqrt[1/6]) = 65.905157° at {3} between co and trip:   arccos(sqrt(3/8)) = 52.238756°
Face vector	16, 42, 42, 16
Confer	uniform relative: spid   related segmentochora: tet || tricu   {6} || trip   hotet aoho   tetacho   related CRFs: gyspid   oct || co || tet   tet || co || cube   tet || co || co   tetaco ausrip   related blends: hocoaso   general polytopal classes: segmentochora   lace simplices
External links

Incidence matrix according to Dynkin symbol

xx3oo3ox&#x   → height = sqrt(5/8) = 0.790569
(tet || co)

o.3o.3o.    | 4  * ♦ 3  3  0  0 | 3  6  3 0 0 0 | 1 3 3 1 0
.o3.o3.o    | * 12 | 0  1  2  2 | 0  2  2 1 2 1 | 0 1 2 1 1
------------+------+------------+---------------+----------
x. .. ..    | 2  0 | 6  *  *  * | 2  2  0 0 0 0 | 1 2 1 0 0
oo3oo3oo&#x | 1  1 | * 12  *  * | 0  2  2 0 0 0 | 0 1 2 1 0
.x .. ..    | 0  2 | *  * 12  * | 0  1  0 1 1 0 | 0 1 1 0 1
.. .. .x    | 0  2 | *  *  * 12 | 0  0  1 0 1 1 | 0 0 1 1 1
------------+------+------------+---------------+----------
x.3o. ..    | 3  0 | 3  0  0  0 | 4  *  * * * * | 1 1 0 0 0
xx .. ..&#x | 2  2 | 1  2  1  0 | * 12  * * * * | 0 1 1 0 0
.. .. ox&#x | 1  2 | 0  2  0  1 | *  * 12 * * * | 0 0 1 1 0
.x3.o ..    | 0  3 | 0  0  3  0 | *  *  * 4 * * | 0 1 0 0 1
.x .. .x    | 0  4 | 0  0  2  2 | *  *  * * 6 * | 0 0 1 0 1
.. .o3.x    | 0  3 | 0  0  0  3 | *  *  * * * 4 | 0 0 0 1 1
------------+------+------------+---------------+----------
x.3o.3o.    ♦ 4  0 | 6  0  0  0 | 4  0  0 0 0 0 | 1 * * * *
xx3oo ..&#x ♦ 3  3 | 3  3  3  0 | 1  3  0 1 0 0 | * 4 * * *
xx .. ox&#x ♦ 2  4 | 1  4  2  2 | 0  2  2 0 1 0 | * * 6 * *
.. oo3ox&#x ♦ 1  3 | 0  3  0  3 | 0  0  3 0 0 1 | * * * 4 *
.x3.o3.x    ♦ 0 12 | 0  0 12 12 | 0  0  0 4 6 4 | * * * * 1

xx3/2oo3/2ox&#x   → height = sqrt(5/8) = 0.790569
(tet || co)

o.3/2o.3/2o.    | 4  * ♦ 3  3  0  0 | 3  6  3 0 0 0 | 1 3 3 1 0
.o3/2.o3/2.o    | * 12 | 0  1  2  2 | 0  2  2 1 2 1 | 0 1 2 1 1
----------------+------+------------+---------------+----------
x.   ..   ..    | 2  0 | 6  *  *  * | 2  2  0 0 0 0 | 1 2 1 0 0
oo3/2oo3/2oo&#x | 1  1 | * 12  *  * | 0  2  2 0 0 0 | 0 1 2 1 0
.x   ..   ..    | 0  2 | *  * 12  * | 0  1  0 1 1 0 | 0 1 1 0 1
..   ..   .x    | 0  2 | *  *  * 12 | 0  0  1 0 1 1 | 0 0 1 1 1
----------------+------+------------+---------------+----------
x.3/2o.   ..    | 3  0 | 3  0  0  0 | 4  *  * * * * | 1 1 0 0 0
xx   ..   ..&#x | 2  2 | 1  2  1  0 | * 12  * * * * | 0 1 1 0 0
..   ..   ox&#x | 1  2 | 0  2  0  1 | *  * 12 * * * | 0 0 1 1 0
.x3/2.o   ..    | 0  3 | 0  0  3  0 | *  *  * 4 * * | 0 1 0 0 1
.x   ..   .x    | 0  4 | 0  0  2  2 | *  *  * * 6 * | 0 0 1 0 1
..   .o3/2.x    | 0  3 | 0  0  0  3 | *  *  * * * 4 | 0 0 0 1 1
----------------+------+------------+---------------+----------
x.3/2o.3/2o.    ♦ 4  0 | 6  0  0  0 | 4  0  0 0 0 0 | 1 * * * *
xx3/2oo   ..&#x ♦ 3  3 | 3  3  3  0 | 1  3  0 1 0 0 | * 4 * * *
xx   ..   ox&#x ♦ 2  4 | 1  4  2  2 | 0  2  2 0 1 0 | * * 6 * *
..   oo3/2ox&#x ♦ 1  3 | 0  3  0  3 | 0  0  3 0 0 1 | * * * 4 *
.x3/2.o3/2.x    ♦ 0 12 | 0  0 12 12 | 0  0  0 4 6 4 | * * * * 1

oo3ox4so&#x   → height = sqrt(5/8) = 0.790569
(tet || co)

demi( o.3o.4o.    ) | 4  * ♦ 3  3  0  0 | 3  3  6 0 0 0 | 1 1 3 0 3
      .o3.o4.o      | * 12 | 0  1  2  2 | 0  2  2 1 1 2 | 0 1 2 1 1
--------------------+------+------------+---------------+----------
      .. o.4s.      | 2  0 | 6  *  *  * | 2  0  2 0 0 0 | 1 0 1 0 2
demi( oo3oo4oo&#x ) | 1  1 | * 12  *  * | 0  2  2 0 0 0 | 0 1 2 0 1
demi( .. .x ..    ) | 0  2 | *  * 12  * | 0  1  0 1 0 1 | 0 1 1 1 0
demi( .. .x ..    ) | 0  2 | *  *  * 12 | 0  0  1 0 1 1 | 0 0 1 1 1
--------------------+------+------------+---------------+----------
sefa( o.3o.4s.    ) | 3  0 | 3  0  0  0 | 4  *  * * * * | 1 0 0 0 1
demi( .. ox ..&#x ) | 1  2 | 0  2  1  0 | * 12  * * * * | 0 1 1 0 0
sefa( .. ox4so&#x ) | 2  2 | 1  2  0  1 | *  * 12 * * * | 0 0 1 0 1
demi( .o3.x ..    ) | 0  3 | 0  0  3  0 | *  *  * 4 * * | 0 1 0 1 0
demi( .o3.x ..    ) | 0  3 | 0  0  0  3 | *  *  * * 4 * | 0 0 0 1 1
      .. .x4.o      | 0  4 | 0  0  2  2 | *  *  * * * 6 | 0 0 1 1 0
--------------------+------+------------+---------------+----------
      o.3o.4s.      ♦ 4  0 | 6  0  0  0 | 4  0  0 0 0 0 | 1 * * * *
demi( oo3ox ..&#x ) ♦ 1  3 | 0  3  3  0 | 0  3  0 1 0 0 | * 4 * * *
      .. ox4so&#x   ♦ 2  4 | 1  4  2  2 | 0  2  2 0 0 1 | * * 6 * *
      .o3.x4.o      ♦ 0 12 | 0  0 12 12 | 0  0  0 4 4 6 | * * * 1 *
sefa( oo3ox4so&#x ) ♦ 3  3 | 3  3  0  3 | 1  0  3 0 1 0 | * * * * 4

starting figure: oo3ox4xo&#x