| 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 / VRML |
|
| 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 |
|
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
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