Acronym  hicu 
Name  hexagonal cupola 
Circumradius  ∞ i.e. flat in euclidean space 
Vertex figures  [3,4,6,4], [3,4,12] 
Dihedral angles 

Confer 

It either can be thought of as a degenerate 3D segmentotope with zero height, or as a 2D euclidean decomposition of the larger base into smaller bits.
Incidence matrix according to Dynkin symbol
xx6ox&#x → height = 0
({6}  {12})
o.6o.  6 *  2 2 0 0  1 2 1 0
.o6.o  * 12  0 1 1 1  0 1 1 1
+++
x. ..  2 0  6 * * *  1 1 0 0
oo6oo&#x  1 1  * 12 * *  0 1 1 0
.x ..  0 2  * * 6 *  0 1 0 1
.. .x  0 2  * * * 6  0 0 1 1
+++
x.6o.  6 0  6 0 0 0  1 * * *
xx ..&#x  2 2  1 2 1 0  * 6 * *
.. ox&#x  1 2  0 2 0 1  * * 6 *
.x6.x  0 12  0 0 6 6  * * * 1
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