Acronym etedpy
Name elongated tetrahedral bipyramid
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
(at margins)
  • at {3} between tet and trip:   arccos[-sqrt(15)/4] = 165.522488°
  • at {3} between tet and tet:   arccos(1/4) = 75.522488°
  • at {4} between trip and trip:   arccos(1/3) = 70.528779°
Confer pen   tepe   tete   etepy   esquippidpy (n=4)  

Incidence matrix according to Dynkin symbol

oxxo3oooo3oooo&#xt   → outer heights = sqrt(5/8) = 0.790569
                       medial height = 1
(pt || pseudo tet || pseudo tet || pt)

o...3o...3o...    | 1 * * *  4 0 0 0 0 | 6 0 0 0 0 | 4 0 0
.o..3.o..3.o..    | * 4 * * | 1 3 1 0 0 | 3 3 3 0 0 | 3 3 0
..o.3..o.3..o.    | * * 4 * | 0 0 1 3 1 | 0 0 3 3 3 | 0 3 3
...o3...o3...o    | * * * 1  0 0 0 0 4 | 0 0 0 0 6 | 0 0 4
------------------+---------+-----------+-----------+------
oo..3oo..3oo..&#x | 1 1 0 0 | 4 * * * * | 3 0 0 0 0 | 3 0 0
.x.. .... ....    | 0 2 0 0 | * 6 * * * | 1 2 1 0 0 | 2 2 0
.oo.3.oo.3.oo.&#x | 0 1 1 0 | * * 4 * * | 0 0 3 0 0 | 0 3 0
..x. .... ....    | 0 0 2 0 | * * * 6 * | 0 0 1 2 1 | 0 2 2
..oo3..oo3..oo&#x | 0 0 1 1 | * * * * 4 | 0 0 0 0 3 | 0 0 3
------------------+---------+-----------+-----------+------
ox.. .... ....&#x | 1 2 0 0 | 2 1 0 0 0 | 6 * * * * | 2 0 0
.x..3.o.. ....    | 0 3 0 0 | 0 3 0 0 0 | * 4 * * * | 1 1 0
.xx. .... ....&#x | 0 2 2 0 | 0 1 2 1 0 | * * 6 * * | 0 2 0
..x.3..o. ....    | 0 0 3 0 | 0 0 0 3 0 | * * * 4 * | 0 1 1
..xo .... ....&#x | 0 0 2 1 | 0 0 0 1 2 | * * * * 6 | 0 0 2
------------------+---------+-----------+-----------+------
ox..3oo.. ....&#x  1 3 0 0 | 3 3 0 0 0 | 3 1 0 0 0 | 4 * *
.xx.3.oo. ....&#x  0 3 3 0 | 0 3 3 3 0 | 0 1 3 1 0 | * 4 *
..xo3..oo ....&#x  0 0 3 1 | 0 0 0 3 3 | 0 0 0 1 3 | * * 4
or
o...3o...3o...    & | 2 *  4  0 0 |  6 0 0 | 4 0
.o..3.o..3.o..    & | * 8 | 1  3 1 |  3 3 3 | 3 3
--------------------+-----+--------+--------+----
oo..3oo..3oo..&#x & | 1 1 | 8  * * |  3 0 0 | 3 0
.x.. .... ....    & | 0 2 | * 12 * |  1 2 1 | 2 2
.oo.3.oo.3.oo.&#x   | 0 2 | *  * 4 |  0 0 3 | 0 3
--------------------+-----+--------+--------+----
ox.. .... ....&#x & | 1 2 | 2  1 0 | 12 * * | 2 0
.x..3.o.. ....    & | 0 3 | 0  3 0 |  * 8 * | 1 1
.xx. .... ....&#x   | 0 4 | 0  2 2 |  * * 6 | 0 2
--------------------+-----+--------+--------+----
ox..3oo.. ....&#x &  1 3 | 3  3 0 |  3 1 0 | 8 *
.xx.3.oo. ....&#x    0 6 | 0  6 3 |  0 2 3 | * 4

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