Acronym it (old: ikedpy)
Name (line-)ikosahedron-tegum,
icosahedral bipyramid
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dual dope
Dihedral angles
  • at {3} between tet and tet (lacing):   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {3} between tet and tet (across rim):   arccos[(3 sqrt(5)-1)/8] = 44.477512°
Confer
general polytopal classes:
tetrahedrochora   Blind polytopes   bistratic lace towers  

Incidence matrix according to Dynkin symbol

oxo3ooo5ooo&#xt   → both heights = (sqrt(5)-1)/4 = 0.309017
(pt || pseudo ike || pt)

o..3o..5o..    | 1  * *  12  0  0 | 30  0  0 | 20  0
.o.3.o.5.o.    | * 12 *   1  5  1 |  5  5  5 |  5  5
..o3..o3..o    | *  * 1   0  0 12 |  0  0 30 |  0 20
---------------+--------+----------+----------+------
oo.3oo.5oo.&#x | 1  1 0 | 12  *  * |  3  0  0 |  3  0
.x. ... ...    | 0  2 0 |  * 30  * |  1  2  1 |  2  2
.oo3.oo5.oo&#x | 0  1 1 |  *  * 12 |  0  0  3 |  0  3
---------------+--------+----------+----------+------
ox. ... ...&#x | 1  2 0 |  2  1  0 | 30  *  * |  2  0
.x.3.o. ...    | 0  3 0 |  0  3  0 |  * 20  * |  1  1
.xo ... ...&#x | 0  2 1 |  0  1  2 |  *  * 30 |  0  2
---------------+--------+----------+----------+------
ox.3oo. ...&#x  1  3 0 |  3  3  0 |  3  1  0 | 20  *
.xo3.oo ...&#x  0  3 1 |  0  3  3 |  0  1  3 |  * 20
or
o..3o..5o..     & | 2  *  12  0 | 30  0 | 20
.o.3.o.5.o.       | * 12   2  5 | 10  5 | 10
------------------+------+-------+-------+---
oo.3oo.5oo.&#x  & | 1  1 | 24  * |  5  0 |  5
.x. ... ...       | 0  2 |  * 30 |  2  2 |  4
------------------+------+-------+-------+---
ox. ... ...&#x  & | 1  2 |  2  1 | 60  * |  2
.x.3.o. ...       | 0  3 |  0  3 |  * 20 |  2
------------------+------+-------+-------+---
ox.3oo. ...&#x  &  1  3 |  3  3 |  3  1 | 40

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