Acronym turap
Name two rectified-pentachoron cupolaic blend
Circumradius sqrt(3/5) = 0.774597
Lace city
in approx. ASCII-art
o     t   T     o		-- ox3oo3xo (so)
                 
                 
                 
                 
   T         t   		-- pseudo oo3xx3oo (being removed double cover oct)

    \         \
     \         +-- o3x3o (oct)
      +----------- o3o3x (tet)

where:
o = o3o
t = x3o
T = o3x
Confer
blend-component:
rap  
External
links
polytopewiki  

This polychoron indeed is a cupolaic blend of 2 gyrated copies of rap in the pure sense of the term, because not only the bottom base, the oct, here gets doubled and thus withdrawn while reconnecting the according ridges, but also the top base becomes a compound.

Thence as an abstract polytope it comes in 2 types: either that top base is considered as a true compound (type A) or it gets seen as 2 merely corealmic polyhedra (type B)


Incidence matrix according to Dynkin symbol

reduced( (xo)o3(oo)x3(ox)o&#x by ..o3..x3..o)   → height = sqrt(5/8) = 0.790569
(so || pseudo oct)

(type A)

(o.).3(o.).3(o.).    & | 8 *   3  3  0 | 3  3  3 0 | 1 3 1
(..)o3(..)o3(..)o      | * 6   0  4  4 | 0  2  8 4 | 0 4 4
-----------------------+-----+----------+-----------+------
(x.). (..). (..).    & | 2 0 | 12  *  * | 2  1  0 0 | 1 2 0
(o.)o3(o.)o3(o.)o&#x & | 1 1 |  * 24  * | 0  1  2 0 | 0 2 1
(..). (..)x (..).      | 0 2 |  *  * 12 | 0  0  2 2 | 0 2 2
-----------------------+-----+----------+-----------+------
(x.).3(o.). (..).    & | 3 0 |  3  0  0 | 8  *  * * | 1 1 0
(x.)o (..). (..).&#x & | 2 1 |  1  2  0 | * 12  * * | 0 2 0
(..). (o.)x (..).&#x & | 1 2 |  0  2  1 | *  * 24 * | 0 1 1
(..)o3(..)x (..)     & | 0 3 |  0  0  3 | *  *  * 8 | 0 1 1
-----------------------+-----+----------+-----------+------
(xo).3(oo).3(ox).       8 0 | 12  0  0 | 8  0  0 0 | 1 0 0
(x.)o3(o.)x (..).&#x &  3 3 |  3  6  3 | 1  3  3 1 | * 8 *
(..). (o.)x3(o.).&#x &  1 3 |  0  3  3 | 0  0  3 1 | * * 8

reduced( (xo)o3(oo)x3(ox)o&#x by ..o3..x3..o)   → height = sqrt(5/8) = 0.790569
(so || pseudo oct)

(type B)

(o.).3(o.).3(o.).    & | 8 *   3  3  0 | 3  3  3 0 | 1 3 1
(..)o3(..)o3(..)o      | * 6   0  4  4 | 0  2  8 4 | 0 4 4
-----------------------+-----+----------+-----------+------
(x.). (..). (..).    & | 2 0 | 12  *  * | 2  1  0 0 | 1 2 0
(o.)o3(o.)o3(o.)o&#x & | 1 1 |  * 24  * | 0  1  2 0 | 0 2 1
(..). (..)x (..).      | 0 2 |  *  * 12 | 0  0  2 2 | 0 2 2
-----------------------+-----+----------+-----------+------
(x.).3(o.). (..).    & | 3 0 |  3  0  0 | 8  *  * * | 1 1 0
(x.)o (..). (..).&#x & | 2 1 |  1  2  0 | * 12  * * | 0 2 0
(..). (o.)x (..).&#x & | 1 2 |  0  2  1 | *  * 24 * | 0 1 1
(..)o3(..)x (..)     & | 0 3 |  0  0  3 | *  *  * 8 | 0 1 1
-----------------------+-----+----------+-----------+------
(x.).3(o.).3(o.).    &  4 0 |  6  0  0 | 4  0  0 0 | 2 * *
(x.)o3(o.)x (..).&#x &  3 3 |  3  6  3 | 1  3  3 1 | * 8 *
(..). (o.)x3(o.).&#x &  1 3 |  0  3  3 | 0  0  3 1 | * * 8

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