Acronym	tetatricu, tet || tricu, K-4.24
Name	tetrahedron atop trigonal cupola, 0.290215-luna of small prismatodecachoron
Segmentochoron display
Circumradius	1
Lace city in approx. ASCII-art	x3o o3o x3x o3x
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 {6} between tricu and tricu:   arccos(-1/4) = 104.477512° at {3} between tet and tricu:   arccos(1/4) = 75.522488° at {4} between tricu and trip:   arccos(sqrt[1/6]) = 65.905157° at {3} between tricu and trip:   arccos(sqrt(3/8)) = 52.238756°
Face vector	13, 30, 27, 10
Confer	uniform relative: spid   related segmentochora: tet || co   {6} || trip   general polytopal classes: luna   segmentochora
External links

This luna is somehow more general as its fraction comes out to be non-rational: the wedge angle is arccos(-1/4), accordingly that fraction is arccos(-1/4) / 360° = 0.290215.

Incidence matrix according to Dynkin symbol

ooxx3oxxo&#xr   → all heights = sqrt(2/3) = 0.816497

o...3o...     | 1 * * * | 3 3 0 0 0 0 0 0 | 3 3 6 0 0 0 0 0 0 0 | 1 1 3 3 0 0
.o..3.o..     | * 3 * * | 1 0 2 2 0 0 0 0 | 2 0 2 1 1 2 0 0 0 0 | 1 0 1 2 1 0
..o.3..o.     | * * 6 * | 0 0 0 1 1 1 1 0 | 0 0 1 0 1 1 1 1 1 0 | 0 0 1 1 1 1
...o3...o     | * * * 3 | 0 1 0 0 0 0 2 2 | 0 2 2 0 0 0 0 2 1 1 | 0 1 2 1 0 1
--------------+---------+-----------------+---------------------+------------
oo..3oo..&#x  | 1 1 0 0 | 3 * * * * * * * | 2 0 2 0 0 0 0 0 0 0 | 1 0 1 2 0 0
o..o3o..o&#x  | 1 0 0 1 | * 3 * * * * * * | 0 2 2 0 0 0 0 0 0 0 | 0 1 2 1 0 0
.... .x..     | 0 2 0 0 | * * 3 * * * * * | 1 0 0 1 0 1 0 0 0 0 | 1 0 0 1 1 0
.oo.3.oo.&#x  | 0 1 1 0 | * * * 6 * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 0 1 1 1 0
..x. ....     | 0 0 2 0 | * * * * 3 * * * | 0 0 0 0 1 0 1 1 0 0 | 0 0 1 0 1 1
.... ..x.     | 0 0 2 0 | * * * * * 3 * * | 0 0 0 0 0 1 1 0 1 0 | 0 0 0 1 1 1
..oo3..oo&#x  | 0 0 1 1 | * * * * * * 6 * | 0 0 1 0 0 0 0 1 1 0 | 0 0 1 1 0 1
...x ....     | 0 0 0 2 | * * * * * * * 3 | 0 1 0 0 0 0 0 1 0 1 | 0 1 1 0 0 1
--------------+---------+-----------------+---------------------+------------
.... ox..&#x  | 1 2 0 0 | 2 0 1 0 0 0 0 0 | 3 * * * * * * * * * | 1 0 0 1 0 0
o..x ....&#x  | 1 0 0 2 | 0 2 0 0 0 0 0 1 | * 3 * * * * * * * * | 0 1 1 0 0 0
oooo3oooo&#xr | 1 1 1 1 | 1 1 0 1 0 0 1 0 | * * 6 * * * * * * * | 0 0 1 1 0 0
.o..3.x..     | 0 3 0 0 | 0 0 3 0 0 0 0 0 | * * * 1 * * * * * * | 1 0 0 0 1 0
.ox. ....&#x  | 0 1 2 0 | 0 0 0 2 1 0 0 0 | * * * * 3 * * * * * | 0 0 1 0 1 0
.... .xx.&#x  | 0 2 2 0 | 0 0 1 2 0 1 0 0 | * * * * * 3 * * * * | 0 0 0 1 1 0
..x.3..x.     | 0 0 6 0 | 0 0 0 0 3 3 0 0 | * * * * * * 1 * * * | 0 0 0 0 1 1
..xx ....&#x  | 0 0 2 2 | 0 0 0 0 1 0 2 1 | * * * * * * * 3 * * | 0 0 1 0 0 1
.... ..xo&#x  | 0 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * * 3 * | 0 0 0 1 0 1
...x3...o     | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * 1 | 0 1 0 0 0 1
--------------+---------+-----------------+---------------------+------------
oo..3ox..&#x  ♦ 1 3 0 0 | 3 0 3 0 0 0 0 0 | 3 0 0 1 0 0 0 0 0 0 | 1 * * * * *
o..x3o..o&#x  ♦ 1 0 0 3 | 0 3 0 0 0 0 0 3 | 0 3 0 0 0 0 0 0 0 1 | * 1 * * * *
ooxx ....&#xr ♦ 1 1 2 2 | 1 2 0 2 1 0 2 1 | 0 1 2 0 1 0 0 1 0 0 | * * 3 * * *
.... oxxo&#xr ♦ 1 2 2 1 | 2 1 1 2 0 1 2 0 | 1 0 2 0 0 1 0 0 1 0 | * * * 3 * *
.ox.3.xx.&#x  ♦ 0 3 6 0 | 0 0 3 6 3 3 0 0 | 0 0 0 1 3 3 1 0 0 0 | * * * * 1 *
..xx3..xo&#x  ♦ 0 0 6 3 | 0 0 0 0 3 3 6 3 | 0 0 0 0 0 0 1 3 3 1 | * * * * * 1

or
o...3o...        | 1 * * | 6 0  0 0 | 6 6 0 0 0 0 | 2 6 0
.o..3.o..      & | * 6 * | 1 2  2 0 | 2 2 1 1 0 0 | 1 3 1
..o.3..o.        | * * 6 | 0 0  2 2 | 0 1 0 2 2 1 | 0 2 2
-----------------+-------+----------+-------------+------
oo..3oo..&#x   & | 1 1 0 | 6 *  * * | 2 2 0 0 0 0 | 1 3 0
.... .x..      & | 0 2 0 | * 6  * * | 1 0 1 0 1 0 | 1 1 1
.oo.3.oo.&#x   & | 0 1 1 | * * 12 * | 0 1 0 1 1 0 | 0 2 1
..x. ....      & | 0 0 2 | * *  * 6 | 0 0 0 1 1 1 | 0 1 2
-----------------+-------+----------+-------------+------
.... ox..&#x   & | 1 2 0 | 2 1  0 0 | 6 * * * * * | 1 1 0
oooo3oooo&#xr    | 1 2 1 | 2 0  2 0 | * 6 * * * * | 0 2 0
.o..3.x..      & | 0 3 0 | 0 3  0 0 | * * 2 * * * | 1 0 1
.ox. ....&#x   & | 0 1 2 | 0 0  2 1 | * * * 6 * * | 0 1 1
.... .xx.&#x   & | 0 2 2 | 0 1  2 1 | * * * * 6 * | 0 1 1
..x.3..x.        | 0 0 6 | 0 0  0 6 | * * * * * 1 | 0 0 2
-----------------+-------+----------+-------------+------
oo..3ox..&#x   & ♦ 1 3 0 | 3 3  0 0 | 3 0 1 0 0 0 | 2 * *
ooxx ....&#xr  & ♦ 1 3 2 | 3 1  4 1 | 1 2 0 1 1 0 | * 6 *
.ox.3.xx.&#x   & ♦ 0 3 6 | 0 3  6 6 | 0 0 1 3 3 1 | * * 2

tet || tricu   → height = sqrt(5/8) = 0.790569

o...3o...     | 1 * * * | 3 3 0 0 0 0 0 0 | 3 3 6 0 0 0 0 0 0 0 | 1 1 3 3 0 0
.o..3.o..     | * 3 * * | 1 0 2 2 0 0 0 0 | 2 0 2 1 1 2 0 0 0 0 | 1 0 1 2 1 0
..o.3..o.     | * * 6 * | 0 0 0 1 1 1 1 0 | 0 0 1 0 1 1 1 1 1 0 | 0 0 1 1 1 1
...o3...o     | * * * 3 | 0 1 0 0 0 0 2 2 | 0 2 2 0 0 0 0 2 1 1 | 0 1 2 1 0 1
--------------+---------+-----------------+---------------------+------------
oo..3oo..&#x  | 1 1 0 0 | 3 * * * * * * * | 2 0 2 0 0 0 0 0 0 0 | 1 0 1 2 0 0
o..o3o..o&#x  | 1 0 0 1 | * 3 * * * * * * | 0 2 2 0 0 0 0 0 0 0 | 0 1 2 1 0 0
.... .x..     | 0 2 0 0 | * * 3 * * * * * | 1 0 0 1 0 1 0 0 0 0 | 1 0 0 1 1 0
.oo.3.oo.&#x  | 0 1 1 0 | * * * 6 * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 0 1 1 1 0
..x. ....     | 0 0 2 0 | * * * * 3 * * * | 0 0 0 0 1 0 1 1 0 0 | 0 0 1 0 1 1
.... ..x.     | 0 0 2 0 | * * * * * 3 * * | 0 0 0 0 0 1 1 0 1 0 | 0 0 0 1 1 1
..oo3..oo&#x  | 0 0 1 1 | * * * * * * 6 * | 0 0 1 0 0 0 0 1 1 0 | 0 0 1 1 0 1
...x ....     | 0 0 0 2 | * * * * * * * 3 | 0 1 0 0 0 0 0 1 0 1 | 0 1 1 0 0 1
--------------+---------+-----------------+---------------------+------------
.... ox..&#x  | 1 2 0 0 | 2 0 1 0 0 0 0 0 | 3 * * * * * * * * * | 1 0 0 1 0 0
o..x ....&#x  | 1 0 0 2 | 0 2 0 0 0 0 0 1 | * 3 * * * * * * * * | 0 1 1 0 0 0
oooo3oooo&#xr | 1 1 1 1 | 1 1 0 1 0 0 1 0 | * * 6 * * * * * * * | 0 0 1 1 0 0
.o..3.x..     | 0 3 0 0 | 0 0 3 0 0 0 0 0 | * * * 1 * * * * * * | 1 0 0 0 1 0
.ox. ....&#x  | 0 1 2 0 | 0 0 0 2 1 0 0 0 | * * * * 3 * * * * * | 0 0 1 0 1 0
.... .xx.&#x  | 0 2 2 0 | 0 0 1 2 0 1 0 0 | * * * * * 3 * * * * | 0 0 0 1 1 0
..x.3..x.     | 0 0 6 0 | 0 0 0 0 3 3 0 0 | * * * * * * 1 * * * | 0 0 0 0 1 1
..xx ....&#x  | 0 0 2 2 | 0 0 0 0 1 0 2 1 | * * * * * * * 3 * * | 0 0 1 0 0 1
.... ..xo&#x  | 0 0 2 1 | 0 0 0 0 0 1 2 0 | * * * * * * * * 3 * | 0 0 0 1 0 1
...x3...o     | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * * * 1 | 0 1 0 0 0 1
--------------+---------+-----------------+---------------------+------------
oo..3ox..&#x  ♦ 1 3 0 0 | 3 0 3 0 0 0 0 0 | 3 0 0 1 0 0 0 0 0 0 | 1 * * * * *
o..x3o..o&#x  ♦ 1 0 0 3 | 0 3 0 0 0 0 0 3 | 0 3 0 0 0 0 0 0 0 1 | * 1 * * * *
ooxx ....&#xr ♦ 1 1 2 2 | 1 2 0 2 1 0 2 1 | 0 1 2 0 1 0 0 1 0 0 | * * 3 * * *
.... oxxo&#xr ♦ 1 2 2 1 | 2 1 1 2 0 1 2 0 | 1 0 2 0 0 1 0 0 1 0 | * * * 3 * *
.ox.3.xx.&#x  ♦ 0 3 6 0 | 0 0 3 6 3 3 0 0 | 0 0 0 1 3 3 1 0 0 0 | * * * * 1 *
..xx3..xo&#x  ♦ 0 0 6 3 | 0 0 0 0 3 3 6 3 | 0 0 0 0 0 0 1 3 3 1 | * * * * * 1