Acronym gyescu, J23
Name gyroelongated square cupola
  
 © ©
Vertex figures [3,43], [34,4], [33,8]
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Face vector 20, 44, 26
Confer
uniform relative:
oap  
blend-component:
squacu   oap  
related Johnson solids:
squacu   gyesquibcu  
general polytopal classes:
Johnson solids   bistratic lace towers  
External
links 		wikipedia   polytopewiki   mathworld   quickfur  

Incidence matrix according to Dynkin symbol

oxo8sox&#xt   → height(1,2) = 1/sqrt(2) = 0.707107
                height(2,3) = sqrt[(1+2*cos(π/8))/(2+2*cos(π/8))] = 0.860296
({4} || pseudo {8} || dual {8})

demi( o..8o..    ) | 4 * * * * | 2 1 1 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0
demi( .o.8.o.    ) | * 4 * * * | 0 1 0 2 0 1 1 0 0 0 0 | 0 1 1 1 1 1 0 0
demi( .o.8.o.    ) | * * 4 * * | 0 0 1 0 2 0 0 1 1 0 0 | 0 1 1 1 1 0 1 0
demi( ..o8..o    ) | * * * 4 * | 0 0 0 0 0 1 0 1 0 2 0 | 0 0 0 1 0 1 1 1
demi( ..o8..o    ) | * * * * 4 | 0 0 0 0 0 0 1 0 1 0 2 | 0 0 0 0 1 1 1 1
-------------------+-----------+-----------------------+----------------
sefa( o..8s..    ) | 2 0 0 0 0 | 4 * * * * * * * * * * | 1 1 0 0 0 0 0 0
demi( oo.8oo.&#x ) | 1 1 0 0 0 | * 4 * * * * * * * * * | 0 1 1 0 0 0 0 0
demi( oo.8oo.&#x ) | 1 0 1 0 0 | * * 4 * * * * * * * * | 0 1 1 0 0 0 0 0
demi( .x. ...    ) | 0 2 0 0 0 | * * * 4 * * * * * * * | 0 1 0 1 0 0 0 0
demi( .x. ...    ) | 0 0 2 0 0 | * * * * 4 * * * * * * | 0 0 1 0 1 0 0 0
      .oo8.oo&#x   | 0 1 0 1 0 | * * * * * 4 * * * * * | 0 0 0 1 0 0 1 0
      .oo8.oo&#x   | 0 1 0 0 1 | * * * * * * 4 * * * * | 0 0 0 1 0 1 0 0
      .oo8.oo&#x   | 0 0 1 1 0 | * * * * * * * 4 * * * | 0 0 0 0 1 1 0 0
      .oo8.oo&#x   | 0 0 1 0 1 | * * * * * * * * 4 * * | 0 0 0 0 1 0 1 0
demi( ... ..x    ) | 0 0 0 2 0 | * * * * * * * * * 4 * | 0 0 0 0 0 1 0 1
demi( ... ..x    ) | 0 0 0 0 2 | * * * * * * * * * * 4 | 0 0 0 0 0 0 1 1
-------------------+-----------+-----------------------+----------------
      o..8s..      | 4 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * * *
sefa( ox.8so.&#x ) | 2 1 1 0 0 | 1 1 1 1 0 0 0 0 0 0 0 | * 4 * * * * * *
demi( ox. ...&#x ) | 1 1 1 0 0 | 0 1 1 0 1 0 0 0 0 0 0 | * * 4 * * * * *
demi( .xo ...&#x ) | 0 1 1 1 0 | 0 0 0 1 0 1 1 0 0 0 0 | * * * 4 * * * *
demi( .xo ...&#x ) | 0 1 1 0 1 | 0 0 0 0 1 0 0 1 1 0 0 | * * * * 4 * * *
demi( ... .ox&#x ) | 0 1 0 1 1 | 0 0 0 0 0 0 1 1 0 1 0 | * * * * * 4 * *
demi( ... .ox&#x ) | 0 0 1 1 1 | 0 0 0 0 0 1 0 0 1 0 1 | * * * * * * 4 *
      ..o8..x      | 0 0 0 4 4 | 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * 1

or
demi( o..8o..    ) | 4 * * * | 2 2 0 0 0 0 0 | 1 2 1 0 0 0 0
      .o.8.o.      | * 8 * * | 0 1 1 1 1 1 0 | 0 1 1 1 1 1 0
demi( ..o8..o    ) | * * 4 * | 0 0 0 0 2 0 2 | 0 0 0 1 0 2 1
demi( ..o8..o    ) | * * * 4 | 0 0 0 0 0 2 2 | 0 0 0 0 1 2 1
-------------------+---------+---------------+--------------
sefa( o..8s..    ) | 2 0 0 0 | 4 * * * * * * | 1 1 0 0 0 0 0
      oo.8oo.&#x   | 1 1 0 0 | * 8 * * * * * | 0 1 1 0 0 0 0
demi( .x. ...    ) | 0 2 0 0 | * * 4 * * * * | 0 1 0 1 0 0 0
demi( .x. ...    ) | 0 2 0 0 | * * * 4 * * * | 0 0 1 0 1 0 0
      .oo8.oo&#x   | 0 1 1 0 | * * * * 8 * * | 0 0 0 1 0 1 0
      .oo8.oo&#x   | 0 1 0 1 | * * * * * 8 * | 0 0 0 0 1 1 0
      ... ..x      | 0 0 1 1 | * * * * * * 8 | 0 0 0 0 0 1 1
-------------------+---------+---------------+--------------
      o..8s..      | 4 0 0 0 | 4 0 0 0 0 0 0 | 1 * * * * * *
sefa( ox.8so.&#x ) | 2 2 0 0 | 1 2 1 0 0 0 0 | * 4 * * * * *
      ox. ...&#x   | 1 2 0 0 | 0 2 0 1 0 0 0 | * * 4 * * * *
demi( .xo ...&#x ) | 0 2 1 0 | 0 0 1 0 2 0 0 | * * * 4 * * *
demi( .xo ...&#x ) | 0 2 0 1 | 0 0 0 1 0 2 0 | * * * * 4 * *
      ... .ox&#x   | 0 1 1 1 | 0 0 0 0 1 1 1 | * * * * * 8 *
      ..o8..x      | 0 0 4 4 | 0 0 0 0 0 0 8 | * * * * * * 1

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