Acronym epobro, J42
Name elongated pentagonal orthobirotunda
 
 © ©
Vertex figure [(3,5)2], [3,42,5]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {3} and {4}:   arccos(-sqrt[(10+2 sqrt(5))/15]) = 169.187683°
  • between {5} and {4}:   arccos(-2/sqrt(5)) = 153.434949°
  • between {4} and {4}:   144°
  • between {3} and {5}:   arccos(-sqrt[(5+2 sqrt(5))/15]) = 142.622632°
Confer
uniform relative:
id   dip  
related Johnson solids:
pero   epro   pobro  
general polytopal classes:
Johnson solids  
External
links
wikipedia   mathworld   quickfur  

Incidence matrix according to Dynkin symbol

xoxxox5ofxxfo&#xt   → height(1,2) = height(5,6) = sqrt[(5-sqrt(5))/10] = 0.525731
                      height(2,3) = height(4,5) = sqrt[(5+sqrt(5))/10] = 0.850651
                      height(3,4) = 1
({5} || pseudo dual f-{5} || pseudo {10} || pseudo {10} || pseudo dual f-{5} || para {5})

o.....5o.....     | 5 *  *  * * * | 2  2  0 0 0  0 0 0  0  0 0 | 1 2 1 0 0 0 0 0 0 0
.o....5.o....     | * 5  *  * * * | 0  2  2 0 0  0 0 0  0  0 0 | 0 1 2 1 0 0 0 0 0 0
..o...5..o...     | * * 10  * * * | 0  0  1 1 1  1 0 0  0  0 0 | 0 0 1 1 1 1 0 0 0 0
...o..5...o..     | * *  * 10 * * | 0  0  0 0 0  1 1 1  1  0 0 | 0 0 0 0 1 1 1 1 0 0
....o.5....o.     | * *  *  * 5 * | 0  0  0 0 0  0 0 0  2  2 0 | 0 0 0 0 0 0 1 2 1 0
.....o5.....o     | * *  *  * * 5 | 0  0  0 0 0  0 0 0  0  2 2 | 0 0 0 0 0 0 0 1 2 1
------------------+---------------+----------------------------+--------------------
x.....5o.....     | 2 0  0  0 0 0 | 5  *  * * *  * * *  *  * * | 1 1 0 0 0 0 0 0 0 0
oo....5oo....&#x  | 1 1  0  0 0 0 | * 10  * * *  * * *  *  * * | 0 1 1 0 0 0 0 0 0 0
.oo...5.oo...&#x  | 0 1  1  0 0 0 | *  * 10 * *  * * *  *  * * | 0 0 1 1 0 0 0 0 0 0
..x... ......     | 0 0  2  0 0 0 | *  *  * 5 *  * * *  *  * * | 0 0 0 1 1 0 0 0 0 0
...... ..x...     | 0 0  2  0 0 0 | *  *  * * 5  * * *  *  * * | 0 0 1 0 0 1 0 0 0 0
..oo..5..oo..&#x  | 0 0  1  1 0 0 | *  *  * * * 10 * *  *  * * | 0 0 0 0 1 1 0 0 0 0
...x.. ......     | 0 0  0  2 0 0 | *  *  * * *  * 5 *  *  * * | 0 0 0 0 1 0 1 0 0 0
...... ...x..     | 0 0  0  2 0 0 | *  *  * * *  * * 5  *  * * | 0 0 0 0 0 1 0 1 0 0
...oo.5...oo.&#x  | 0 0  0  1 1 0 | *  *  * * *  * * * 10  * * | 0 0 0 0 0 0 1 1 0 0
....oo5....oo&#x  | 0 0  0  0 1 1 | *  *  * * *  * * *  * 10 * | 0 0 0 0 0 0 0 1 1 0
.....x ......     | 0 0  0  0 0 2 | *  *  * * *  * * *  *  * 5 | 0 0 0 0 0 0 0 0 1 1
------------------+---------------+----------------------------+--------------------
x.....5o.....     | 5 0  0  0 0 0 | 5  0  0 0 0  0 0 0  0  0 0 | 1 * * * * * * * * *
xo.... ......&#x  | 2 1  0  0 0 0 | 1  2  0 0 0  0 0 0  0  0 0 | * 5 * * * * * * * *
...... ofx...&#xt | 1 2  2  0 0 0 | 0  2  2 0 1  0 0 0  0  0 0 | * * 5 * * * * * * *
.ox... ......&#x  | 0 1  2  0 0 0 | 0  0  2 1 0  0 0 0  0  0 0 | * * * 5 * * * * * *
..xx.. ......&#x  | 0 0  2  2 0 0 | 0  0  0 1 0  2 1 0  0  0 0 | * * * * 5 * * * * *
...... ..xx..&#x  | 0 0  2  2 0 0 | 0  0  0 0 1  2 0 1  0  0 0 | * * * * * 5 * * * *
...xo. ......&#x  | 0 0  0  2 1 0 | 0  0  0 0 0  0 1 0  2  0 0 | * * * * * * 5 * * *
...... ...xfo&#xt | 0 0  0  2 2 1 | 0  0  0 0 0  0 0 1  2  2 0 | * * * * * * * 5 * *
....ox ......&#x  | 0 0  0  0 1 2 | 0  0  0 0 0  0 0 0  0  2 1 | * * * * * * * * 5 *
.....x5.....o     | 0 0  0  0 0 5 | 0  0  0 0 0  0 0 0  0  0 5 | * * * * * * * * * 1
or
o.....5o.....      & | 10  *  * |  2  2  0  0  0  0 | 1  2  1  0 0 0
.o....5.o....      & |  * 10  * |  0  2  2  0  0  0 | 0  1  2  1 0 0
..o...5..o...      & |  *  * 20 |  0  0  1  1  1  1 | 0  0  1  1 1 1
---------------------+----------+-------------------+---------------
x.....5o.....      & |  2  0  0 | 10  *  *  *  *  * | 1  1  0  0 0 0
oo....5oo....&#x   & |  1  1  0 |  * 20  *  *  *  * | 0  1  1  0 0 0
.oo...5.oo...&#x   & |  0  1  1 |  *  * 20  *  *  * | 0  0  1  1 0 0
..x... ......      & |  0  0  2 |  *  *  * 10  *  * | 0  0  0  1 1 0
...... ..x...      & |  0  0  2 |  *  *  *  * 10  * | 0  0  1  0 0 1
..oo..5..oo..&#x     |  0  0  2 |  *  *  *  *  * 10 | 0  0  0  0 1 1
---------------------+----------+-------------------+---------------
x.....5o.....      & |  5  0  0 |  5  0  0  0  0  0 | 2  *  *  * * *
xo.... ......&#x   & |  2  1  0 |  1  2  0  0  0  0 | * 10  *  * * *
...... ofx...&#xt  & |  1  2  2 |  0  2  2  0  1  0 | *  * 10  * * *
.ox... ......&#x   & |  0  1  2 |  0  0  2  1  0  0 | *  *  * 10 * *
..xx.. ......&#x     |  0  0  4 |  0  0  0  2  0  2 | *  *  *  * 5 *
...... ..xx..&#x     |  0  0  4 |  0  0  0  0  2  2 | *  *  *  * * 5

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