Acronym eikedpy
Name elongated icosahedral bipyramid
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°
Confer it   eikepy  

Incidence matrix according to Dynkin symbol

oxxo3oooo5oooo&#xt   → outer heights = (sqrt(5)-1)/4 = 0.309017
                       medial height = 1
(pt || pseudo ike || pseudo ike || pt)

o...3o...5o...    | 1  *  * *  12  0  0  0  0 | 30  0  0  0  0 | 20  0  0
.o..3.o..5.o..    | * 12  * * |  1  5  1  0  0 |  5  5  5  0  0 |  5  5  0
..o.3..o.5..o.    | *  * 12 * |  0  0  1  5  1 |  0  0  5  5  5 |  0  5  5
...o3...o5...o    | *  *  * 1   0  0  0  0 12 |  0  0  0  0 30 |  0  0 20
------------------+-----------+----------------+----------------+---------
oo..3oo..5oo..&#x | 1  1  0 0 | 12  *  *  *  * |  5  0  0  0  0 |  5  0  0
.x.. .... ....    | 0  2  0 0 |  * 30  *  *  * |  1  2  1  0  0 |  2  2  0
.oo.3.oo.5.oo.&#x | 0  1  1 0 |  *  * 12  *  * |  0  0  5  0  0 |  0  5  0
..x. .... ....    | 0  0  2 0 |  *  *  * 30  * |  0  0  1  2  1 |  0  2  2
..oo3..oo5..oo&#x | 0  0  1 1 |  *  *  *  * 12 |  0  0  0  0  5 |  0  0  5
------------------+-----------+----------------+----------------+---------
ox.. .... ....&#x | 1  2  0 0 |  2  1  0  0  0 | 30  *  *  *  * |  2  0  0
.x..3.o.. ....    | 0  3  0 0 |  0  3  0  0  0 |  * 20  *  *  * |  1  1  0
.xx. .... ....&#x | 0  2  2 0 |  0  1  2  1  0 |  *  * 30  *  * |  0  2  0
..x.3..o. ....    | 0  0  3 0 |  0  0  0  3  0 |  *  *  * 20  * |  0  1  1
..xo .... ....&#x | 0  0  2 1 |  0  0  0  1  2 |  *  *  *  * 30 |  0  0  2
------------------+-----------+----------------+----------------+---------
ox..3oo.. ....&#x  1  3  0 0 |  3  3  0  0  0 |  3  1  0  0  0 | 20  *  *
.xx.3.oo. ....&#x  0  3  3 0 |  0  3  3  3  0 |  0  1  3  1  0 |  * 20  *
..xo3..oo ....&#x  0  0  3 1 |  0  0  0  3  3 |  0  0  0  1  3 |  *  * 20
or
o...3o...5o...    & | 2  *  12  0  0 | 30  0  0 | 20  0
.o..3.o..5.o..    & | * 24 |  1  5  1 |  5  5  5 |  5  5
--------------------+------+----------+----------+------
oo..3oo..5oo..&#x & | 1  1 | 24  *  * |  5  0  0 |  5  0
.x.. .... ....    & | 0  2 |  * 60  * |  1  2  1 |  2  2
.oo.3.oo.5.oo.&#x   | 0  2 |  *  * 12 |  0  0  5 |  0  5
--------------------+------+----------+----------+------
ox.. .... ....&#x & | 1  2 |  2  1  0 | 60  *  * |  2  0
.x..3.o.. ....    & | 0  3 |  0  3  0 |  * 40  * |  1  1
.xx. .... ....&#x   | 0  4 |  0  2  2 |  *  * 30 |  0  2
--------------------+------+----------+----------+------
ox..3oo.. ....&#x &  1  3 |  3  3  0 |  3  1  0 | 40  *
.xx.3.oo. ....&#x    0  6 |  0  6  3 |  0  2  3 |  * 20

© 2004-2019
top of page