Acronym eikepy
Name elongated icosahedral pyramid
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {3} between tet and tet:   arccos[-(1+3 sqrt(5))/8] = 164.477512°
  • at {4} between trip and trip:   arccos(-sqrt(5)/3) = 138.189685°
  • at {3} between tet and trip:   arccos(sqrt[9-3 sqrt(5)]/4) = 112.238756°
  • at {3} between ike and trip:   90°
Face vector 25, 84, 100, 41
Confer
segmentochora:
ikepy   ipe  
related CRFs:
eikedpy  
general polytopal classes:
bistratic lace towers  

Incidence matrix according to Dynkin symbol

oxx3ooo5ooo&#xt   → pyramid height = (sqrt(5)-1)/4 = 0.309017
                    prism height = 1
(pt || pseudo ike || ike)

o..3o..5o..    | 1  *  * ♦ 12  0  0  0 | 30  0  0  0 | 20  0 0
.o.3.o.5.o.    | * 12  * |  1  5  1  0 |  5  5  5  0 |  5  5 0
..o3..o5..o    | *  * 12 |  0  0  1  5 |  0  0  5  5 |  0  5 1
---------------+---------+-------------+-------------+--------
oo.3oo.5oo.&#x | 1  1  0 | 12  *  *  * |  5  0  0  0 |  5  0 0
.x. ... ...    | 0  2  0 |  * 30  *  * |  1  2  1  0 |  2  2 0
.oo3.oo5.oo&#x | 0  1  1 |  *  * 12  * |  0  0  5  0 |  0  5 0
..x ... ...    | 0  0  2 |  *  *  * 30 |  0  0  1  2 |  0  2 1
---------------+---------+-------------+-------------+--------
ox. ... ...&#x | 1  2  0 |  2  1  0  0 | 30  *  *  * |  2  0 0
.x.3.o. ...    | 0  3  0 |  0  3  0  0 |  * 20  *  * |  1  1 0
.xx ... ...&#x | 0  2  2 |  0  1  2  1 |  *  * 30  * |  0  2 0
..x3..o ...    | 0  0  3 |  0  0  0  3 |  *  *  * 20 |  0  1 1
---------------+---------+-------------+-------------+--------
ox.3oo. ...&#x ♦ 1  3  0 |  3  3  0  0 |  3  1  0  0 | 20  * *
.xx3.oo ...&#x ♦ 0  3  3 |  0  3  3  3 |  0  1  3  1 |  * 20 *
..x3..o5..o    ♦ 0  0 12 |  0  0  0 30 |  0  0  0 20 |  *  * 1

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