Acronym	papadoe, pap || doe, K-4.81
Name	pentagonal-antiprism atop dodecahedron, parabidiminished segment of vertex-first hexacosachoron, pentagonal-antiprism-first cap of grand antiprism
Segmentochoron display
Circumradius	(1+sqrt(5))/2 = 1.618034
Lace city in approx. ASCII-art	o5x x5o x5o f5o o5f o5x
Face vector	30, 100, 114, 44
Confer	uniform relative: ex   gap   related segmentochora: ikadoe   general polytopal classes: segmentochora

Incidence matrix according to Dynkin symbol

pap || doe   → height = 1/2

o.5o.       .... ....     | 5 * * * * * | 2  2  2  2 1 0 0  0  0 0 0  0 0 0 | 1 2 2 2 1  2  2 1  2  2 0 0 0  0  0 0 0 0 0 0 | 1 2 1 2 1  2 1 0 0 0 0
.o5.o       .... ....     | * 5 * * * * | 0  2  0  0 0 2 1  2  2 0 0  0 0 0 | 0 1 0 0 2  2  2 0  0  0 1 2 2  2  2 1 0 0 0 0 | 1 1 0 0 2  2 0 1 2 1 0
.. ..       o...5o...     | * * 5 * * * | 0  0  2  0 0 0 0  0  0 2 1  0 0 0 | 0 0 1 0 0  0  0 2  2  0 0 0 0  0  0 0 1 2 0 0 | 0 0 1 1 0  0 2 0 0 0 1
.. ..       .o..5.o..     | * * * 5 * * | 0  0  0  2 0 0 1  0  0 0 1  2 0 0 | 0 0 0 1 0  2  0 0  2  2 0 0 0  2  0 0 0 2 1 0 | 0 1 0 1 0  2 2 0 0 1 1
.. ..       ..o.5..o.     | * * * * 5 * | 0  0  0  0 1 0 0  2  0 0 0  2 1 0 | 0 0 0 0 0  0  2 0  0  2 0 1 0  2  2 0 0 1 2 0 | 0 0 0 0 1  2 1 0 1 2 1
.. ..       ...o5...o     | * * * * * 5 | 0  0  0  0 0 0 0  0  2 0 0  0 1 2 | 0 0 0 0 0  0  0 0  0  0 0 0 1  0  2 2 0 0 2 1 | 0 0 0 0 0  0 0 1 1 2 1
--------------------------+-------------+-----------------------------------+-----------------------------------------------+-----------------------
x. ..       .... ....     | 2 0 0 0 0 0 | 5  *  *  * * * *  *  * * *  * * * | 1 1 1 1 0  0  0 0  0  0 0 0 0  0  0 0 0 0 0 0 | 1 1 1 1 0  0 0 0 0 0 0
oo5oo&#x    .... ....     | 1 1 0 0 0 0 | * 10  *  * * * *  *  * * *  * * * | 0 1 0 0 1  1  1 0  0  0 0 0 0  0  0 0 0 0 0 0 | 1 1 0 0 1  1 0 0 0 0 0
o.5o.    || o...5o...     | 1 0 1 0 0 0 | *  * 10  * * * *  *  * * *  * * * | 0 0 1 0 0  0  0 1  1  0 0 0 0  0  0 0 0 0 0 0 | 0 0 1 1 0  0 1 0 0 0 0
o.5o.    || .o..5.o..     | 1 0 0 1 0 0 | *  *  * 10 * * *  *  * * *  * * * | 0 0 0 1 0  1  0 0  1  1 0 0 0  0  0 0 0 0 0 0 | 0 1 0 1 0  1 1 0 0 0 0
o.5o.    || ..o.5..o.     | 1 0 0 0 1 0 | *  *  *  * 5 * *  *  * * *  * * * | 0 0 0 0 0  0  2 0  0  2 0 0 0  0  0 0 0 0 0 0 | 0 0 0 0 1  2 1 0 0 0 0
.. .x       .... ....     | 0 2 0 0 0 0 | *  *  *  * * 5 *  *  * * *  * * * | 0 0 0 0 1  0  0 0  0  0 1 1 1  0  0 0 0 0 0 0 | 1 0 0 0 1  0 0 1 1 0 0
.o5.o    || .o..5.o..     | 0 1 0 1 0 0 | *  *  *  * * * 5  *  * * *  * * * | 0 0 0 0 0  2  0 0  0  0 0 0 0  2  0 0 0 0 0 0 | 0 1 0 0 0  2 0 0 0 1 0
.o5.o    || ..o.5..o.     | 0 1 0 0 1 0 | *  *  *  * * * * 10  * * *  * * * | 0 0 0 0 0  0  1 0  0  0 0 1 0  1  1 0 0 0 0 0 | 0 0 0 0 1  1 0 0 1 1 0
.o5.o    || ...o5...o     | 0 1 0 0 0 1 | *  *  *  * * * *  * 10 * *  * * * | 0 0 0 0 0  0  0 0  0  0 0 0 1  0  1 1 0 0 0 0 | 0 0 0 0 0  0 0 1 1 1 0
.. ..       .... x...     | 0 0 2 0 0 0 | *  *  *  * * * *  *  * 5 *  * * * | 0 0 0 0 0  0  0 1  0  0 0 0 0  0  0 0 1 1 0 0 | 0 0 1 0 0  0 1 0 0 0 1
.. ..       oo..5oo..&#x  | 0 0 1 1 0 0 | *  *  *  * * * *  *  * * 5  * * * | 0 0 0 0 0  0  0 0  2  0 0 0 0  0  0 0 0 2 0 0 | 0 0 0 1 0  0 2 0 0 0 1
.. ..       .oo.5.oo.&#x  | 0 0 0 1 1 0 | *  *  *  * * * *  *  * * * 10 * * | 0 0 0 0 0  0  0 0  0  1 0 0 0  1  0 0 0 1 1 0 | 0 0 0 0 0  1 1 0 0 1 1
.. ..       ..oo5..oo&#x  | 0 0 0 0 1 1 | *  *  *  * * * *  *  * * *  * 5 * | 0 0 0 0 0  0  0 0  0  0 0 0 0  0  2 0 0 0 2 0 | 0 0 0 0 0  0 0 0 1 2 1
.. ..       ...x ....     | 0 0 0 0 0 2 | *  *  *  * * * *  *  * * *  * * 5 | 0 0 0 0 0  0  0 0  0  0 0 0 0  0  0 1 0 0 1 1 | 0 0 0 0 0  0 0 1 0 1 1
--------------------------+-------------+-----------------------------------+-----------------------------------------------+-----------------------
x.5o.       .... ....     | 5 0 0 0 0 0 | 5  0  0  0 0 0 0  0  0 0 0  0 0 0 | 1 * * * *  *  * *  *  * * * *  *  * * * * * * | 1 0 1 0 0  0 0 0 0 0 0
xo ..&#x    .... ....     | 2 1 0 0 0 0 | 1  2  0  0 0 0 0  0  0 0 0  0 0 0 | * 5 * * *  *  * *  *  * * * *  *  * * * * * * | 1 1 0 0 0  0 0 0 0 0 0
x. ..    || o... ....     | 2 0 1 0 0 0 | 1  0  2  0 0 0 0  0  0 0 0  0 0 0 | * * 5 * *  *  * *  *  * * * *  *  * * * * * * | 0 0 1 1 0  0 0 0 0 0 0
x. ..    || .o.. ....     | 2 0 0 1 0 0 | 1  0  0  2 0 0 0  0  0 0 0  0 0 0 | * * * 5 *  *  * *  *  * * * *  *  * * * * * * | 0 1 0 1 0  0 0 0 0 0 0
.. ox&#x    .... ....     | 1 2 0 0 0 0 | 0  2  0  0 0 1 0  0  0 0 0  0 0 0 | * * * * 5  *  * *  *  * * * *  *  * * * * * * | 1 0 0 0 1  0 0 0 0 0 0
oo5oo&#x || .o..5.o..     | 1 1 0 1 0 0 | 0  1  0  1 0 0 1  0  0 0 0  0 0 0 | * * * * * 10  * *  *  * * * *  *  * * * * * * | 0 1 0 0 0  1 0 0 0 0 0
oo5oo&#x || ..o.5..o.     | 1 1 0 0 1 0 | 0  1  0  0 1 0 0  1  0 0 0  0 0 0 | * * * * *  * 10 *  *  * * * *  *  * * * * * * | 0 0 0 0 1  1 0 0 0 0 0
.. o.    || .... x...     | 1 0 2 0 0 0 | 0  0  2  0 0 0 0  0  0 1 0  0 0 0 | * * * * *  *  * 5  *  * * * *  *  * * * * * * | 0 0 1 0 0  0 1 0 0 0 0
o.5o.    || oo..5oo..&#x  | 1 0 1 1 0 0 | 0  0  1  1 0 0 0  0  0 0 1  0 0 0 | * * * * *  *  * * 10  * * * *  *  * * * * * * | 0 0 0 1 0  0 1 0 0 0 0
o.5o.    || .oo.5.oo.&#x  | 1 0 0 1 1 0 | 0  0  0  1 1 0 0  0  0 0 0  1 0 0 | * * * * *  *  * *  * 10 * * *  *  * * * * * * | 0 0 0 0 0  1 1 0 0 0 0
.o5.x       .... ....     | 0 5 0 0 0 0 | 0  0  0  0 0 5 0  0  0 0 0  0 0 0 | * * * * *  *  * *  *  * 1 * *  *  * * * * * * | 1 0 0 0 0  0 0 1 0 0 0
.. .x    || .... ..o.     | 0 2 0 0 1 0 | 0  0  0  0 0 1 0  2  0 0 0  0 0 0 | * * * * *  *  * *  *  * * 5 *  *  * * * * * * | 0 0 0 0 1  0 0 0 1 0 0
.. .x    || .... ...o     | 0 2 0 0 0 1 | 0  0  0  0 0 1 0  0  2 0 0  0 0 0 | * * * * *  *  * *  *  * * * 5  *  * * * * * * | 0 0 0 0 0  0 0 1 1 0 0
.o5.o    || .oo.5.oo.&#x  | 0 1 0 1 1 0 | 0  0  0  0 0 0 1  1  0 0 0  1 0 0 | * * * * *  *  * *  *  * * * * 10  * * * * * * | 0 0 0 0 0  1 0 0 0 1 0
.o5.o    || ..oo5..oo&#x  | 0 1 0 0 1 1 | 0  0  0  0 0 0 0  1  1 0 0  0 1 0 | * * * * *  *  * *  *  * * * *  * 10 * * * * * | 0 0 0 0 0  0 0 0 1 1 0
.o ..    || ...x ....     | 0 1 0 0 0 2 | 0  0  0  0 0 0 0  0  2 0 0  0 0 1 | * * * * *  *  * *  *  * * * *  *  * 5 * * * * | 0 0 0 0 0  0 0 1 0 1 0
.. ..       o...5x...     | 0 0 5 0 0 0 | 0  0  0  0 0 0 0  0  0 5 0  0 0 0 | * * * * *  *  * *  *  * * * *  *  * * 1 * * * | 0 0 1 0 0  0 0 0 0 0 1
.. ..       .... xfo.&#xt | 0 0 2 2 1 0 | 0  0  0  0 0 0 0  0  0 1 2  2 0 0 | * * * * *  *  * *  *  * * * *  *  * * * 5 * * | 0 0 0 0 0  0 1 0 0 0 1
.. ..       .ofx ....&#xt | 0 0 0 1 2 2 | 0  0  0  0 0 0 0  0  0 0 0  2 2 1 | * * * * *  *  * *  *  * * * *  *  * * * * 5 * | 0 0 0 0 0  0 0 0 0 1 1
.. ..       ...x5...o     | 0 0 0 0 0 5 | 0  0  0  0 0 0 0  0  0 0 0  0 0 5 | * * * * *  *  * *  *  * * * *  *  * * * * * 1 | 0 0 0 0 0  0 0 1 0 0 1
--------------------------+-------------+-----------------------------------+-----------------------------------------------+-----------------------
xo5ox&#x    .... ....     ♦ 5 5 0 0 0 0 | 5 10  0  0 0 5 0  0  0 0 0  0 0 0 | 1 5 0 0 5  0  0 0  0  0 1 0 0  0  0 0 0 0 0 0 | 1 * * * *  * * * * * *
xo ..&#x || .o.. ....     ♦ 2 1 0 1 0 0 | 1  2  0  2 0 0 1  0  0 0 0  0 0 0 | 0 1 0 1 0  2  0 0  0  0 0 0 0  0  0 0 0 0 0 0 | * 5 * * *  * * * * * *
x.5o.    || o...5x...     ♦ 5 0 5 0 0 0 | 5  0 10  0 0 0 0  0  0 5 0  0 0 0 | 1 0 5 0 0  0  0 5  0  0 0 0 0  0  0 0 1 0 0 0 | * * 1 * *  * * * * * *
x. ..    || oo..5oo..&#x  ♦ 2 0 1 1 0 0 | 1  0  2  2 0 0 0  0  0 0 1  0 0 0 | 0 0 1 1 0  0  0 0  2  0 0 0 0  0  0 0 0 0 0 0 | * * * 5 *  * * * * * *
.. ox&#x || ..o.5..o.     ♦ 1 2 0 0 1 0 | 0  2  0  0 1 1 0  2  0 0 0  0 0 0 | 0 0 0 0 1  0  2 0  0  0 0 1 0  0  0 0 0 0 0 0 | * * * * 5  * * * * * *
oo5oo&#x || .oo.5.oo.&#x  ♦ 1 1 0 1 1 0 | 0  1  0  1 1 0 1  1  0 0 0  1 0 0 | 0 0 0 0 0  1  1 0  0  1 0 0 0  1  0 0 0 0 0 0 | * * * * * 10 * * * * *
.. o.    || .... xfo.&#xt ♦ 1 0 2 2 1 0 | 0  0  2  2 1 0 0  0  0 1 2  2 0 0 | 0 0 0 0 0  0  0 1  2  2 0 0 0  0  0 0 0 1 0 0 | * * * * *  * 5 * * * *
.o5.x    || ...x5...o     ♦ 0 5 0 0 0 5 | 0  0  0  0 0 5 0  0 10 0 0  0 0 5 | 0 0 0 0 0  0  0 0  0  0 1 0 5  0  0 5 0 0 0 1 | * * * * *  * * 1 * * *
.. .x    || ..oo5..oo&#x  ♦ 0 2 0 0 1 1 | 0  0  0  0 0 1 0  2  2 0 0  0 1 0 | 0 0 0 0 0  0  0 0  0  0 0 1 1  0  2 0 0 0 0 0 | * * * * *  * * * 5 * *
.o ..    || .ofx ....&#xt ♦ 0 1 0 1 2 2 | 0  0  0  0 0 0 1  2  2 0 0  2 2 1 | 0 0 0 0 0  0  0 0  0  0 0 0 0  2  2 1 0 0 1 0 | * * * * *  * * * * 5 *
.. ..       oofx5xfoo&#xt ♦ 0 0 5 5 5 5 | 0  0  0  0 0 0 0  0  0 5 5 10 5 5 | 0 0 0 0 0  0  0 0  0  0 0 0 0  0  0 0 1 5 5 1 | * * * * *  * * * * * 1

or
o.5o.       .... ....     & | 10  *  * |  2  2  2  2  1  0  0  0 | 1  3  2  2  4  1  2  2 0  0 | 1  3 1  2  2  1 0
.. ..       o...5o...     & |  * 10  * |  0  0  2  0  0  2  1  0 | 0  0  1  0  0  2  2  0 1  2 | 0  0 1  1  0  2 1
.. ..       .o..5.o..     & |  *  * 10 |  0  0  0  2  1  0  1  2 | 0  0  0  1  2  0  2  4 0  3 | 0  1 0  1  2  3 1
----------------------------+----------+-------------------------+-----------------------------+------------------
x. ..       .... ....     & |  2  0  0 | 10  *  *  *  *  *  *  * | 1  1  1  1  0  0  0  0 0  0 | 1  1 1  1  0  0 0
oo5oo&#x    .... ....       |  2  0  0 |  * 10  *  *  *  *  *  * | 0  2  0  0  2  0  0  0 0  0 | 1  2 0  0  1  0 0
o.5o.    || o...5o...     & |  1  1  0 |  *  * 20  *  *  *  *  * | 0  0  1  0  0  1  1  0 0  0 | 0  0 1  1  0  1 0
o.5o.    || .o..5.o..     & |  1  0  1 |  *  *  * 20  *  *  *  * | 0  0  0  1  1  0  1  1 0  0 | 0  1 0  1  1  1 0
o.5o.    || ..o.5..o.     & |  1  0  1 |  *  *  *  * 10  *  *  * | 0  0  0  0  2  0  0  2 0  0 | 0  1 0  0  2  1 0
.. ..       .... x...     & |  0  2  0 |  *  *  *  *  * 10  *  * | 0  0  0  0  0  1  0  0 1  1 | 0  0 1  0  0  1 1
.. ..       oo..5oo..&#x  & |  0  1  1 |  *  *  *  *  *  * 10  * | 0  0  0  0  0  0  2  0 0  2 | 0  0 0  1  0  2 1
.. ..       .oo.5.oo.&#x    |  0  0  2 |  *  *  *  *  *  *  * 10 | 0  0  0  0  0  0  0  2 0  2 | 0  0 0  0  1  2 1
----------------------------+----------+-------------------------+-----------------------------+------------------
x.5o.       .... ....     & |  5  0  0 |  5  0  0  0  0  0  0  0 | 2  *  *  *  *  *  *  * *  * | 1  0 1  0  0  0 0
xo ..&#x    .... ....     & |  3  0  0 |  1  2  0  0  0  0  0  0 | * 10  *  *  *  *  *  * *  * | 1  1 0  0  0  0 0
x. ..    || o... ....     & |  2  1  0 |  1  0  2  0  0  0  0  0 | *  * 10  *  *  *  *  * *  * | 0  0 1  1  0  0 0
x. ..    || .o.. ....     & |  2  0  1 |  1  0  0  2  0  0  0  0 | *  *  * 10  *  *  *  * *  * | 0  1 0  1  0  0 0
oo5oo&#x || .o..5.o..     & |  2  0  1 |  0  1  0  1  1  0  0  0 | *  *  *  * 20  *  *  * *  * | 0  1 0  0  1  0 0
.. o.    || .... x...     & |  1  2  0 |  0  0  2  0  0  1  0  0 | *  *  *  *  * 10  *  * *  * | 0  0 1  0  0  1 0
o.5o.    || oo..5oo..&#x  & |  1  1  1 |  0  0  1  1  0  0  1  0 | *  *  *  *  *  * 20  * *  * | 0  0 0  1  0  1 0
o.5o.    || .oo.5.oo.&#x  & |  1  0  2 |  0  0  0  1  1  0  0  1 | *  *  *  *  *  *  * 20 *  * | 0  0 0  0  1  1 0
.. ..       o...5x...     & |  0  5  0 |  0  0  0  0  0  5  0  0 | *  *  *  *  *  *  *  * 2  * | 0  0 1  0  0  0 1
.. ..       .... xfo.&#xt & |  0  2  3 |  0  0  0  0  0  1  2  2 | *  *  *  *  *  *  *  * * 10 | 0  0 0  0  0  1 1
----------------------------+----------+-------------------------+-----------------------------+------------------
xo5ox&#x    .... ....       ♦ 10  0  0 | 10 10  0  0  0  0  0  0 | 2 10  0  0  0  0  0  0 0  0 | 1  * *  *  *  * *
xo ..&#x || .o.. ....     & ♦  3  0  1 |  1  2  0  2  1  0  0  0 | 0  1  0  1  2  0  0  0 0  0 | * 10 *  *  *  * *
x.5o.    || o...5x...     & ♦  5  5  0 |  5  0 10  0  0  5  0  0 | 1  0  5  0  0  5  0  0 1  0 | *  * 2  *  *  * *
x. ..    || oo..5oo..&#x  & ♦  2  1  1 |  1  0  2  2  0  0  1  0 | 0  0  1  1  0  0  2  0 0  0 | *  * * 10  *  * *
oo5oo&#x || .oo.5.oo.&#x    ♦  2  0  2 |  0  1  0  2  2  0  0  1 | 0  0  0  0  2  0  0  2 0  0 | *  * *  * 10  * *
.. o.    || .... xfo.&#xt & ♦  1  2  3 |  0  0  2  2  1  1  2  2 | 0  0  0  0  0  1  2  2 0  1 | *  * *  *  * 10 *
.. ..       oofx5xfoo&#xt   ♦  0 10 10 |  0  0  0  0  0 10 10 10 | 0  0  0  0  0  0  0  0 2 10 | *  * *  *  *  * 1