Acronym n-gytpuf
Name n-gonal gyrotegmicupolafastegium,
n-cupola atop inverted gyrated n-cupola,
2n-prismatic gyrated bi-wedge
 
 ©
Lace city
in approx. ASCII-art
     x-n-x     
x-n-o     o-n-x
     x-n-x     
Especially dygytpuf (n=2)*   tregytpuf (n=3)   squagytpuf (n=4)   pegytpuf (n=5)  
Confer
related segmentochora:
n-puf  

The lace city display shows that this polychoron can be dissected vertically into segmentochoric components: into 2 n-pufs; thereby adding one 2n-prism as further facet each, which here occurs as internal pseudo facet only. In fact, the other way round, this polychoron well can be considered as an external blend of those 2 components.

* Even so the orientation as stack of n-cupolae shows that those are all monostratic, except of the case n=2 those would not be segmentochora. This is because of the needed shift of these generally non-degenerate bases out of their circumcenter. Accordingly in general there will be no (full-dimensional) circumradius either. (But be aware, that the incidence matrices for n=2 would differ because of the degenerate n-gon.)


Incidence matrix according to Dynkin symbol

ox-n-xx&#x || xx-n-xo&#x   (1.243647<n<5.104299)   → height = ???
(n-cu || inv gyro n-cu)

o.-n-o.      ..   ..    | n  *  * * | 2  2  2 0 0  0  0 0 0  0 0 | 1 1 2 1 2  2 0 0 0  0 0 0 0 0 0 0 | 1 1 1 2 0 0 0 0
.o-n-.o      ..   ..    | * 2n  * * | 0  1  0 1 1  1  1 0 0  0 0 | 0 1 1 0 0  1 1 1 1  1 1 1 0 0 0 0 | 1 0 1 1 1 1 1 0
..   ..      o.-n-o.    | *  * 2n * | 0  0  1 0 0  1  0 1 1  1 0 | 0 0 0 1 1  1 0 1 1  1 0 0 1 1 1 0 | 0 1 1 1 0 1 1 1
..   ..      .o-n-.o    | *  *  * n | 0  0  0 0 0  0  2 0 0  2 2 | 0 0 0 0 0  0 0 0 0  2 2 1 0 2 1 1 | 0 0 0 0 1 2 1 1
------------------------+-----------+----------------------------+-----------------------------------+----------------
..   x.      ..   ..    | 2  0  0 0 | n  *  * * *  *  * * *  * * | 1 0 1 0 1  0 0 0 0  0 0 0 0 0 0 0 | 1 1 0 1 0 0 0 0
oo-n-oo&#x   ..   ..    | 1  1  0 0 | * 2n  * * *  *  * * *  * * | 0 1 1 0 0  1 0 0 0  0 0 0 0 0 0 0 | 1 0 1 1 0 0 0 0
o.-n-o.    || o.-n-o.    | 1  0  1 0 | *  * 2n * *  *  * * *  * * | 0 0 0 1 1  1 0 0 0  0 0 0 0 0 0 0 | 0 1 1 1 0 0 0 0
.x   ..      ..   ..    | 0  2  0 0 | *  *  * n *  *  * * *  * * | 0 1 0 0 0  0 1 1 0  0 1 0 0 0 0 0 | 1 0 1 0 1 1 0 0
..   .x      ..   ..    | 0  2  0 0 | *  *  * * n  *  * * *  * * | 0 0 1 0 0  0 1 0 1  0 0 1 0 0 0 0 | 1 0 0 1 1 0 1 0
.o-n-.o    || o.-n-o.    | 0  1  1 0 | *  *  * * * 2n  * * *  * * | 0 0 0 0 0  1 0 1 1  1 0 0 0 0 0 0 | 0 0 1 1 0 1 1 0
.o-n-.o    || .o-n-.o    | 0  1  0 1 | *  *  * * *  * 2n * *  * * | 0 0 0 0 0  0 0 0 0  1 1 1 0 0 0 0 | 0 0 0 0 1 1 1 0
..   ..      x.   ..    | 0  0  2 0 | *  *  * * *  *  * n *  * * | 0 0 0 1 0  0 0 1 0  0 0 0 1 1 0 0 | 0 1 1 0 0 1 0 1
..   ..      ..   x.    | 0  0  2 0 | *  *  * * *  *  * * n  * * | 0 0 0 0 1  0 0 0 1  0 0 0 1 0 1 0 | 0 1 0 1 0 0 1 1
..   ..      oo-n-oo&#x | 0  0  1 1 | *  *  * * *  *  * * * 2n * | 0 0 0 0 0  0 0 0 0  1 0 0 0 1 1 0 | 0 0 0 0 0 1 1 1
..   ..      .x   ..    | 0  0  0 2 | *  *  * * *  *  * * *  * n | 0 0 0 0 0  0 0 0 0  0 1 0 0 1 0 1 | 0 0 0 0 1 1 0 1
------------------------+-----------+----------------------------+-----------------------------------+----------------
o.-n-x.      ..   ..    | n  0  0 0 | n  0  0 0 0  0  0 0 0  0 0 | 1 * * * *  * * * *  * * * * * * * | 1 1 0 0 0 0 0 0
ox   ..&#x   ..   ..    | 1  2  0 0 | 0  2  0 1 0  0  0 0 0  0 0 | * n * * *  * * * *  * * * * * * * | 1 0 1 0 0 0 0 0
..   xx&#x   ..   ..    | 2  2  0 0 | 1  2  0 0 1  0  0 0 0  0 0 | * * n * *  * * * *  * * * * * * * | 1 0 0 1 0 0 0 0
o.-n-o.    || x.   ..    | 1  0  2 0 | 0  0  2 0 0  0  0 1 0  0 0 | * * * n *  * * * *  * * * * * * * | 0 1 1 0 0 0 0 0
..   x.    || ..   x.    | 2  0  2 0 | 1  0  2 0 0  0  0 0 1  0 0 | * * * * n  * * * *  * * * * * * * | 0 1 0 1 0 0 0 0
oo-n-oo&#x || o.-n-o.    | 1  1  1 0 | 0  1  1 0 0  1  0 0 0  0 0 | * * * * * 2n * * *  * * * * * * * | 0 0 1 1 0 0 0 0
.x-n-.x      ..   ..    | 0 2n  0 0 | 0  0  0 n n  0  0 0 0  0 0 | * * * * *  * 1 * *  * * * * * * * | 1 0 0 0 1 0 0 0
.x   ..    || x.   ..    | 0  2  2 0 | 0  0  0 1 0  2  0 1 0  0 0 | * * * * *  * * n *  * * * * * * * | 0 0 1 0 0 1 0 0
..   .x    || ..   x.    | 0  2  2 0 | 0  0  0 0 1  2  0 0 1  0 0 | * * * * *  * * * n  * * * * * * * | 0 0 0 1 0 0 1 0
.o-n-.o    || oo-n-oo&#x | 0  1  1 1 | 0  0  0 0 0  1  1 0 0  1 0 | * * * * *  * * * * 2n * * * * * * | 0 0 0 0 0 1 1 0
.x   ..    || .x   ..    | 0  2  0 2 | 0  0  0 1 0  0  2 0 0  0 1 | * * * * *  * * * *  * n * * * * * | 0 0 0 0 1 1 0 0
..   .x    || .o-n-.o    | 0  2  0 1 | 0  0  0 0 1  0  2 0 0  0 0 | * * * * *  * * * *  * * n * * * * | 0 0 0 0 1 0 1 0
..   ..      x.-n-x.    | 0  0 2n 0 | 0  0  0 0 0  0  0 n n  0 0 | * * * * *  * * * *  * * * 1 * * * | 0 1 0 0 0 0 0 1
..   ..      xx   ..&#x | 0  0  2 2 | 0  0  0 0 0  0  0 1 0  2 1 | * * * * *  * * * *  * * * * n * * | 0 0 0 0 0 1 0 1
..   ..      ..   xo&#x | 0  0  2 1 | 0  0  0 0 0  0  0 0 1  2 0 | * * * * *  * * * *  * * * * * n * | 0 0 0 0 0 0 1 1
..   ..      .x-n-.o    | 0  0  0 n | 0  0  0 0 0  0  0 0 0  0 n | * * * * *  * * * *  * * * * * * 1 | 0 0 0 0 1 0 0 1
------------------------+-----------+----------------------------+-----------------------------------+----------------
ox-n-xx&#x   ..   ..     n 2n  0 0 | n 2n  0 n n  0  0 0 0  0 0 | 1 n n 0 0  0 1 0 0  0 0 0 0 0 0 0 | 1 * * * * * * *
o.-n-x.    || x.-n-x.     n  0 2n 0 | n  0 2n 0 0  0  0 n n  0 0 | 1 0 0 n n  0 0 0 0  0 0 0 1 0 0 0 | * 1 * * * * * *
ox   ..&#x || x.   ..     1  2  2 0 | 0  2  2 1 0  2  0 1 0  0 0 | 0 1 0 1 0  2 0 1 0  0 0 0 0 0 0 0 | * * n * * * * *
..   xx&#x || ..   x.     2  2  2 0 | 1  2  2 0 1  2  0 0 1  0 0 | 0 0 1 0 1  2 0 0 1  0 0 0 0 0 0 0 | * * * n * * * *
.x-n-.x    || .x-n-.o     0 2n  0 n | 0  0  0 n n  0 2n 0 0  0 n | 0 0 0 0 0  0 1 0 0  0 n n 0 0 0 1 | * * * * 1 * * *
.x   ..    || xx   ..&#x  0  2  2 2 | 0  0  0 1 0  2  2 1 0  2 1 | 0 0 0 0 0  0 0 1 0  2 1 0 0 1 0 0 | * * * * * n * *
..   .x    || ..   xo&#x  0  2  2 1 | 0  0  0 0 1  2  2 0 1  2 0 | 0 0 0 0 0  0 0 0 1  2 0 1 0 0 1 0 | * * * * * * n *
..   ..      xx-n-xo&#x  0  0 2n n | 0  0  0 0 0  0  0 n n 2n n | 0 0 0 0 0  0 0 0 0  0 0 0 1 n n 1 | * * * * * * * 1


xxo-n-oxx oxo&#xt   (1.243647<n<5.104299)   → both heights = sqrt[3 - 1/sin2(π/n)]/2
({n} || pseudo {2n}-p || dual {n})

o..-n-o.. o..    | n  * * | 2  4  0  0  0  0 0 | 1  4  2  2 0 0 0  0  0  0 0 | 2 2 1 0 0 0
.o.-n-.o. .o.    | * 4n * | 0  1  1  1  1  1 0 | 0  1  1  1 1 1 1  1  1  1 0 | 1 1 1 1 1 1
..o-n-..o ..o    | *  * n | 0  0  0  0  0  4 2 | 0  0  0  0 0 0 0  2  4  2 1 | 0 0 0 2 1 2
-----------------+--------+--------------------+-----------------------------+------------
x..   ... ...    | 2  0 0 | n  *  *  *  *  * * | 1  2  0  0 0 0 0  0  0  0 0 | 2 1 0 0 0 0
oo.-n-oo. oo.&#x | 1  1 0 | * 4n  *  *  *  * * | 0  1  1  1 0 0 0  0  0  0 0 | 1 1 1 0 0 0
.x.   ... ...    | 0  2 0 | *  * 2n  *  *  * * | 0  1  0  0 1 1 0  1  0  0 0 | 1 1 0 1 1 0
...   .x. ...    | 0  2 0 | *  *  * 2n  *  * * | 0  0  1  0 1 0 1  0  1  0 0 | 1 0 1 1 0 1
...   ... .x.    | 0  2 0 | *  *  *  * 2n  * * | 0  0  0  1 0 1 1  0  0  1 0 | 0 1 1 0 1 1
.oo-n-.oo .oo&#x | 0  1 1 | *  *  *  *  * 4n * | 0  0  0  0 0 0 0  1  1  1 0 | 0 0 0 1 1 1
...   ..x ...    | 0  0 2 | *  *  *  *  *  * n | 0  0  0  0 0 0 0  0  2  0 1 | 0 0 0 2 0 1
-----------------+--------+--------------------+-----------------------------+------------
x..-n-o.. ...    | n  0 0 | n  0  0  0  0  0 0 | 1  *  *  * * * *  *  *  * * | 2 0 0 0 0 0
xx.   ... ...&#x | 2  2 0 | 1  2  1  0  0  0 0 | * 2n  *  * * * *  *  *  * * | 1 1 0 0 0 0
...   ox. ...&#x | 1  2 0 | 0  2  0  1  0  0 0 | *  * 2n  * * * *  *  *  * * | 1 0 1 0 0 0
...   ... ox.&#x | 1  2 0 | 0  2  0  0  1  0 0 | *  *  * 2n * * *  *  *  * * | 0 1 1 0 0 0
.x.-n-.x. ...    | 0 2n 0 | 0  0  n  n  0  0 0 | *  *  *  * 2 * *  *  *  * * | 1 0 0 1 0 0
.x.   ... .x.    | 0  4 0 | 0  0  2  0  2  0 0 | *  *  *  * * n *  *  *  * * | 0 1 0 0 1 0
...   .x. .x.    | 0  4 0 | 0  0  0  2  2  0 0 | *  *  *  * * * n  *  *  * * | 0 0 1 0 0 1
.xo   ... ...&#x | 0  2 1 | 0  0  1  0  0  2 0 | *  *  *  * * * * 2n  *  * * | 0 0 0 1 1 0
...   .xx ...&#x | 0  2 2 | 0  0  0  1  0  2 1 | *  *  *  * * * *  * 2n  * * | 0 0 0 1 0 1
...   ... .xo&#x | 0  2 1 | 0  0  0  0  1  2 0 | *  *  *  * * * *  *  * 2n * | 0 0 0 0 1 1
..o-n-..x ...    | 0  0 n | 0  0  0  0  0  0 n | *  *  *  * * * *  *  *  * 1 | 0 0 0 2 0 0
-----------------+--------+--------------------+-----------------------------+------------
xx.-n-ox. ...&#x  n 2n 0 | n 2n  n  n  0  0 0 | 1  n  n  0 1 0 0  0  0  0 0 | 2 * * * * *
xx.   ... ox.&#x  2  4 0 | 1  4  2  0  2  0 0 | 0  2  0  2 0 1 0  0  0  0 0 | * n * * * *
...   ox. ox.&#x  1  4 0 | 0  4  0  2  2  0 0 | 0  0  2  2 0 0 1  0  0  0 0 | * * n * * *
.xo-n-.xx ...&#x  0 2n n | 0  0  n  n  0 2n n | 0  0  0  0 1 0 0  n  n  0 1 | * * * 2 * *
.xo   ... .xo&#x  0  4 1 | 0  0  2  0  2  4 0 | 0  0  0  0 0 1 0  2  0  2 0 | * * * * n *
...   .xx .xo&#x  0  4 2 | 0  0  0  2  2  4 1 | 0  0  0  0 0 0 1  0  2  2 0 | * * * * * n

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