Acronym	gyepcu, J24
Name	gyroelongated pentagonal cupola
	© ©
Vertex figures	[3,4,5,4], [34,4], [33,10]
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Face vector	25, 55, 32
Confer	uniform relative: dap   blend-component: pecu   dap   related Johnson solids: pecu   gyepibcu   general polytopal classes: Johnson solids   bistratic lace towers
External links

Incidence matrix according to Dynkin symbol

oxo10sox&#xt   → height(1,2) = sqrt((5-sqrt(5))/10) = 0.525731
                 height(2,3) = sqrt[(1+2*cos(π/10))/(2+2*cos(π/10))] = 0.862397
({5} || pseudo {10} || dual {10})

demi( o..10o..    ) | 5 * * * * | 2 1 1 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0
demi( .o.10.o.    ) | * 5 * * * | 0 1 0 2 0 1 1 0 0 0 0 | 0 1 1 1 1 1 0 0
demi( .o.10.o.    ) | * * 5 * * | 0 0 1 0 2 0 0 1 1 0 0 | 0 1 1 1 1 0 1 0
demi( ..o10..o    ) | * * * 5 * | 0 0 0 0 0 1 0 1 0 2 0 | 0 0 0 1 0 1 1 1
demi( ..o10..o    ) | * * * * 5 | 0 0 0 0 0 0 1 0 1 0 2 | 0 0 0 0 1 1 1 1
--------------------+-----------+-----------------------+----------------
sefa( o..10s..    ) | 2 0 0 0 0 | 5 * * * * * * * * * * | 1 1 0 0 0 0 0 0
demi( oo.10oo.&#x ) | 1 1 0 0 0 | * 5 * * * * * * * * * | 0 1 1 0 0 0 0 0
demi( oo.10oo.&#x ) | 1 0 1 0 0 | * * 5 * * * * * * * * | 0 1 1 0 0 0 0 0
demi( .x.  ...    ) | 0 2 0 0 0 | * * * 5 * * * * * * * | 0 1 0 1 0 0 0 0
demi( .x.  ...    ) | 0 0 2 0 0 | * * * * 5 * * * * * * | 0 0 1 0 1 0 0 0
      .oo10.oo&#x   | 0 1 0 1 0 | * * * * * 5 * * * * * | 0 0 0 1 0 0 1 0
      .oo10.oo&#x   | 0 1 0 0 1 | * * * * * * 5 * * * * | 0 0 0 1 0 1 0 0
      .oo10.oo&#x   | 0 0 1 1 0 | * * * * * * * 5 * * * | 0 0 0 0 1 1 0 0
      .oo10.oo&#x   | 0 0 1 0 1 | * * * * * * * * 5 * * | 0 0 0 0 1 0 1 0
demi( ...  ..x    ) | 0 0 0 2 0 | * * * * * * * * * 5 * | 0 0 0 0 0 1 0 1
demi( ...  ..x    ) | 0 0 0 0 2 | * * * * * * * * * * 5 | 0 0 0 0 0 0 1 1
--------------------+-----------+-----------------------+----------------
      o..10s..      | 5 0 0 0 0 | 5 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * *
sefa( ox.10so.&#x ) | 2 1 1 0 0 | 1 1 1 1 0 0 0 0 0 0 0 | * 5 * * * * * *
demi( ox.  ...&#x ) | 1 1 1 0 0 | 0 1 1 0 1 0 0 0 0 0 0 | * * 5 * * * * *
demi( .xo  ...&#x ) | 0 1 1 1 0 | 0 0 0 1 0 1 1 0 0 0 0 | * * * 5 * * * *
demi( .xo  ...&#x ) | 0 1 1 0 1 | 0 0 0 0 1 0 0 1 1 0 0 | * * * * 5 * * *
demi( ...  .ox&#x ) | 0 1 0 1 1 | 0 0 0 0 0 0 1 1 0 1 0 | * * * * * 5 * *
demi( ...  .ox&#x ) | 0 0 1 1 1 | 0 0 0 0 0 1 0 0 1 0 1 | * * * * * * 5 *
      ..o10..x      | 0 0 0 5 5 | 0 0 0 0 0 0 0 0 0 5 5 | * * * * * * * 1

or
demi( o..10o..    ) | 5  * * * | 2  2 0 0  0  0  0 | 1 2 1 0 0  0 0
      .o.10.o.      | * 10 * * | 0  1 1 1  1  1  0 | 0 1 1 1 1  1 0
demi( ..o10..o    ) | *  * 5 * | 0  0 0 0  2  0  2 | 0 0 0 1 0  2 1
demi( ..o10..o    ) | *  * * 5 | 0  0 0 0  0  2  2 | 0 0 0 0 1  2 1
--------------------+----------+-------------------+---------------
sefa( o..10s..    ) | 2  0 0 0 | 5  * * *  *  *  * | 1 1 0 0 0  0 0
      oo.10oo.&#x   | 1  1 0 0 | * 10 * *  *  *  * | 0 1 1 0 0  0 0
demi( .x.  ...    ) | 0  2 0 0 | *  * 5 *  *  *  * | 0 1 0 1 0  0 0
demi( .x.  ...    ) | 0  2 0 0 | *  * * 5  *  *  * | 0 0 1 0 1  0 0
      .oo10.oo&#x   | 0  1 1 0 | *  * * * 10  *  * | 0 0 0 1 0  1 0
      .oo10.oo&#x   | 0  1 0 1 | *  * * *  * 10  * | 0 0 0 0 1  1 0
      ...  ..x      | 0  0 1 1 | *  * * *  *  * 10 | 0 0 0 0 0  1 1
--------------------+----------+-------------------+---------------
      o..10s..      | 5  0 0 0 | 5  0 0 0  0  0  0 | 1 * * * *  * *
sefa( ox.10so.&#x ) | 2  2 0 0 | 1  2 1 0  0  0  0 | * 5 * * *  * *
      ox.  ...&#x   | 1  2 0 0 | 0  2 0 1  0  0  0 | * * 5 * *  * *
demi( .xo  ...&#x ) | 0  2 1 0 | 0  0 1 0  2  0  0 | * * * 5 *  * *
demi( .xo  ...&#x ) | 0  2 0 1 | 0  0 0 1  0  2  0 | * * * * 5  * *
      ...  .ox&#x   | 0  1 1 1 | 0  0 0 0  1  1  1 | * * * * * 10 *
      ..o10..x      | 0  0 5 5 | 0  0 0 0  0  0 10 | * * * * *  * 1