s8o q-š8o   s8o
               
  o8x     o8x  
               
      x8o      

At the adjoining op the additions of dihedral angles of the blend-components, which in turn have been convex themselves, show the overall convexity:

( oap-8-op|oaf     = arccos[sqrt(2-sqrt(2)+sqrt(2-sqrt(2)))/2] = 54.465321° )   +   ( op-8-squacu|coaop = arccos[-(2-sqrt(2))/2] = 107.031248° )   = 161.496569°
( squippy-4-op|oaf = arccos[-(2 sqrt(2+sqrt(2))-2-sqrt(2))/2] = 98.085593°  )   +   ( op-4-squippy|coaop = arccos[(2-sqrt(2))/2] = 72.968752°  )   = 171.054345°
( squippy-4-op|oaf = arccos[-(2 sqrt(2+sqrt(2))-2-sqrt(2))/2] = 98.085593°  )   +   ( op-4-squap|coaop = arccos[1/sqrt(sqrt(8))] = 53.515624°  )   = 151.601217°

Incidence matrix according to Dynkin symbol

(qo)xo2(sš)ox8(oo)xo&#xt   → height(12,3) = sqrt[2 sqrt(2)-1]/2 = 0.676097
                             height(3,4) = sqrt[2 sqrt(20+14 sqrt(2))-4 sqrt(2)-5]/2 = 0.700077
(co || pseudo op || gyro {8})

demi(  (o.).. (o.)..8(o.)..    ) | 8 *  * * * | 2  2  2  0 0 0 0  0  0 0 | 1 2 1  2 2 1 0 0 0 0 0 0 0  0 0 0 0 | 1 1 2 1 0 0 0 0 0
other( (.o).. (.o)..8(.o)..    ) | * 4  * * * | 0  4  0  4 0 0 0  0  0 0 | 0 2 2  4 0 0 2 2 0 0 0 0 0  0 0 0 0 | 1 2 2 0 1 0 0 0 0
       (..)o. (..)o.8(..)o.      | * * 16 * * | 0  0  1  1 1 1 1  1  1 0 | 0 0 0  1 1 1 1 1 1 1 1 1 1  1 1 1 0 | 0 1 1 1 1 1 1 1 1
demi(  (..).o (..).o8(..).o    ) | * *  * 4 * | 0  0  0  0 0 0 0  4  0 2 | 0 0 0  0 0 0 0 0 0 0 0 2 0  4 2 0 1 | 0 0 0 0 0 2 1 0 2  below {4}
other( (..).o (..).o8(..).o    ) | * *  * * 4 | 0  0  0  0 0 0 0  0  4 2 | 0 0 0  0 0 0 0 0 0 0 0 0 2  4 0 2 1 | 0 0 0 0 0 2 0 1 2  below {3}
---------------------------------+------------+--------------------------+-------------------------------------+------------------
sefa(  (..).. (s.)..8(o.)..    ) | 2 0  0 0 0 | 8  *  *  * * * *  *  * * | 1 1 0  0 1 0 0 0 0 0 0 0 0  0 0 0 0 | 1 0 1 1 0 0 0 0 0
       (oo).. (oo)..8(oo)..&#x   | 1 1  0 0 0 | * 16  *  * * * *  *  * * | 0 1 1  1 0 0 0 0 0 0 0 0 0  0 0 0 0 | 1 1 1 0 0 0 0 0 0
       (o.)o. (o.)o.8(o.)o.&#x   | 1 0  1 0 0 | *  * 16  * * * *  *  * * | 0 0 0  1 1 1 0 0 0 0 0 0 0  0 0 0 0 | 0 1 1 1 0 0 0 0 0
       (.o)o. (.o)o.8(.o)o.&#x   | 0 1  1 0 0 | *  *  * 16 * * *  *  * * | 0 0 0  1 0 0 1 1 0 0 0 0 0  0 0 0 0 | 0 1 1 0 1 0 0 0 0
       (..)x. (..).. (..)..      | 0 0  2 0 0 | *  *  *  * 8 * *  *  * * | 0 0 0  0 0 0 1 0 1 1 0 1 1  0 0 0 0 | 0 1 0 0 1 1 1 1 0
demi(  (..).. (..).. (..)x.    ) | 0 0  2 0 0 | *  *  *  * * 8 *  *  * * | 0 0 0  0 1 0 0 1 1 0 1 0 0  0 1 0 0 | 0 0 1 1 1 0 1 0 1  medial below {4}
other( (..).. (..).. (..)x.    ) | 0 0  2 0 0 | *  *  *  * * * 8  *  * * | 0 0 0  0 0 1 0 0 0 1 1 0 0  0 0 1 0 | 0 1 0 1 0 0 0 1 1  medial below {3}
demi(  (..)oo (..)oo8(..)oo&#x ) | 0 0  1 1 0 | *  *  *  * * * * 16  * * | 0 0 0  0 0 0 0 0 0 0 0 1 0  1 1 0 0 | 0 0 0 0 0 1 1 0 1  below {4}
other( (..)oo (..)oo8(..)oo&#x ) | 0 0  1 0 1 | *  *  *  * * * *  * 16 * | 0 0 0  0 0 0 0 0 0 0 0 0 1  1 0 1 0 | 0 0 0 0 0 1 0 1 1  below {3}
       (..).. (..).x (..)..      | 0 0  0 1 1 | *  *  *  * * * *  *  * 8 | 0 0 0  0 0 0 0 0 0 0 0 0 0  2 0 0 1 | 0 0 0 0 0 1 0 0 2
---------------------------------+------------+--------------------------+-------------------------------------+------------------
       (..).. (s.)..8(o.)..      | 4 0  0 0 0 | 4  0  0  0 0 0 0  0  0 0 | 2 * *  * * * * * * * * * *  * * * * | 1 0 0 1 0 0 0 0 0
sefa1( (..).. (sš)..8(oo)..&#x ) | 2 1  0 0 0 | 1  2  0  0 0 0 0  0  0 0 | * 8 *  * * * * * * * * * *  * * * * | 1 1 0 0 0 0 0 0 0
sefa2( (..).. (sš)..8(oo)..&#x ) | 2 2  0 0 0 | 0  4  0  0 0 0 0  0  0 0 | * * 4  * * * * * * * * * *  * * * * | 1 0 1 0 0 0 0 0 0
       (oo)o. (oo)o.8(oo)o.&#x   | 1 1  1 0 0 | 0  1  1  1 0 0 0  0  0 0 | * * * 16 * * * * * * * * *  * * * * | 0 1 1 0 0 0 0 0 0
sefa1( (..).. (s.)o.8(o.)x.&#x ) | 2 0  2 0 0 | 1  0  2  0 0 1 0  0  0 0 | * * *  * 8 * * * * * * * *  * * * * | 0 0 1 1 0 0 0 0 0  {4}
sefa2( (..).. (s.)o.8(o.)x.&#x ) | 1 0  2 0 0 | 0  0  2  0 0 0 1  0  0 0 | * * *  * * 8 * * * * * * *  * * * * | 0 1 0 1 0 0 0 0 0  {3}
       (.o)x. (..).. (..)..&#x   | 0 1  2 0 0 | 0  0  0  2 1 0 0  0  0 0 | * * *  * * * 8 * * * * * *  * * * * | 0 1 0 0 1 0 0 0 0
demi(  (..).. (..).. (.o)x.&#x ) | 0 1  2 0 0 | 0  0  0  2 0 1 0  0  0 0 | * * *  * * * * 8 * * * * *  * * * * | 0 0 1 0 1 0 0 0 0  below {4}
demi(  (..)x. (..).. (..)x.    ) | 0 0  4 0 0 | 0  0  0  0 2 2 0  0  0 0 | * * *  * * * * * 4 * * * *  * * * * | 0 0 0 0 1 0 1 0 0  below {4}
other( (..)x. (..).. (..)x.    ) | 0 0  4 0 0 | 0  0  0  0 2 0 2  0  0 0 | * * *  * * * * * * 4 * * *  * * * * | 0 1 0 0 0 0 0 1 0  below {3}
       (..).. (..)o.8(..)x.      | 0 0  8 0 0 | 0  0  0  0 0 4 4  0  0 0 | * * *  * * * * * * * 2 * *  * * * * | 0 0 0 1 0 0 0 0 1
demi(  (..)xo (..).. (..)..&#x ) | 0 0  2 1 0 | 0  0  0  0 1 0 0  2  0 0 | * * *  * * * * * * * * 8 *  * * * * | 0 0 0 0 0 1 1 0 0  below {4}
other( (..)xo (..).. (..)..&#x ) | 0 0  2 0 1 | 0  0  0  0 1 0 0  0  2 0 | * * *  * * * * * * * * * 8  * * * * | 0 0 0 0 0 1 0 1 0  below {3}
       (..).. (..)ox (..)..&#x   | 0 0  1 1 1 | 0  0  0  0 0 0 0  1  1 1 | * * *  * * * * * * * * * * 16 * * * | 0 0 0 0 0 1 0 0 1
demi(  (..).. (..).. (..)xo&#x ) | 0 0  2 1 0 | 0  0  0  0 0 1 0  2  0 0 | * * *  * * * * * * * * * *  * 8 * * | 0 0 0 0 0 0 1 0 1  below {4}
other( (..).. (..).. (..)xo&#x ) | 0 0  2 0 1 | 0  0  0  0 0 0 1  0  2 0 | * * *  * * * * * * * * * *  * * 8 * | 0 0 0 0 0 0 0 1 1  below {3}
       (..).. (..).x8(..).o      | 0 0  0 4 4 | 0  0  0  0 0 0 0  0  0 8 | * * *  * * * * * * * * * *  * * * 1 | 0 0 0 0 0 0 0 0 2
---------------------------------+------------+--------------------------+-------------------------------------+------------------
       (qo).. (sš)o.8(oo)x.&#x   ♦ 8 4  0 0 0 | 8 16  0  0 0 0 0  0  0 0 | 2 4 8  0 0 0 0 0 0 0 0 0 0  0 0 0 0 | 1 * * * * * * * *
sefa(  (qo)x. (sš)o.8(oo)x.&#x ) ♦ 2 2  4 0 0 | 0  4  4  4 2 0 2  0  0 0 | 0 1 0  4 0 2 2 0 0 1 0 0 0  0 0 0 0 | * 4 * * * * * * *
sefa(  (..).. (sš)o.8(oo)x.&#x ) ♦ 2 1  2 0 0 | 1  2  2  2 0 1 0  0  0 0 | 0 0 1  2 1 0 0 1 0 0 0 0 0  0 0 0 0 | * * 8 * * * * * *
       (..).. (s.)o.8(o.)x.&#x   ♦ 4 0  8 0 0 | 4  0  8  0 0 4 4  0  0 0 | 1 0 0  0 4 4 0 0 0 0 1 0 0  0 0 0 0 | * * * 2 * * * * *
demi(  (.o)x. (..).. (.o)x.&#x ) ♦ 0 1  4 0 0 | 0  0  0  4 2 2 0  0  0 0 | 0 0 0  0 0 0 2 2 1 0 0 0 0  0 0 0 0 | * * * * 4 * * * *
       (..)xo (..)ox (..)..&#x   ♦ 0 0  2 1 1 | 0  0  0  0 1 0 0  2  2 1 | 0 0 0  0 0 0 0 0 0 0 0 1 1  2 0 0 0 | * * * * * 8 * * *
demi(  (..)xo (..).. (..)xo&#x ) ♦ 0 0  4 1 0 | 0  0  0  0 2 2 0  4  0 0 | 0 0 0  0 0 0 0 0 1 0 0 2 0  0 2 0 0 | * * * * * * 4 * *  below {4}
other( (..)xo (..).. (..)xo&#x ) ♦ 0 0  4 0 1 | 0  0  0  0 2 0 2  0  4 0 | 0 0 0  0 0 0 0 0 0 1 0 0 2  0 0 2 0 | * * * * * * * 4 *  below {3}
       (..).. (..)ox8(..)xo&#x   ♦ 0 0  8 4 4 | 0  0  0  0 0 4 4  8  8 8 | 0 0 0  0 0 0 0 0 0 0 1 0 0  8 4 4 1 | * * * * * * * * 2