Acronym  hippy, 6pyr 
Name  (degenerate) hexagonal pyramid 
Circumradius  ∞ i.e. flat in euclidean space 
Vertex figures  [3^{6}], [3,3,6] 
Dual  (topologically selfdual, in different orientation) 
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
ox6oo&#x → height = 0
(pt  {6})
tip o.6o.  1 *  6 0  6 0
base .o6.o  * 6  1 2  2 1
+++
lace oo6oo&#x  1 1  6 *  2 0
base .x ..  0 2  * 6  1 1
+++
coat ox ..&#x  1 2  2 1  6 *
base .x6.o  0 6  0 6  * 1
ox3ox&#x → height = 0
(pt  {6})
tip o.3o.  1 *  6 0 0  3 3 0
base .o3.o  * 6  1 1 1  1 1 1
+++
lace oo3oo&#x  1 1  6 * *  1 1 0
base .x ..  0 2  * 3 *  1 0 1
base .. .x  0 2  * * 3  0 1 1
+++
coat ox ..&#x  1 2  2 1 0  3 * *
coat ox ..&#x  1 2  2 0 1  * 3 *
base .x6.o  0 6  0 3 3  * * 1
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