Acronym | ..., K-4.146 |
Name |
pentagon - pentagonal-rotunda wedge, {5} || pero |
Segmentochoron display | |
Circumradius | sqrt[5+2 sqrt(5)] = 3.077684 |
Face vector | 25, 65, 58, 18 |
Confer |
|
This polychoron occurs as a bidiminishing of xo3ox5oo&#x: The first diminishing chops off a peppy from the ike, but only scratches a pentagon of id. The second one chops off the complemental part from the ike, then leaving just that pentagonal facet, and chops off a pero from id.
Incidence matrix according to Dynkin symbol
xxox5oofx&#xr → height(1,2) = 1 height(2,3) = height(4,1) = sqrt[(5-sqrt(5))/10] = 0.525731 height(3,4) = sqrt[(5+sqrt(5))/10] = 0.850651 o...5o... | 5 * * * | 2 1 2 2 0 0 0 0 0 | 1 2 2 2 1 2 2 0 0 0 0 0 | 1 1 2 2 1 0 .o..5.o.. | * 5 * * | 0 1 0 0 2 2 0 0 0 | 0 2 0 0 0 2 0 1 2 1 0 0 | 1 0 2 0 1 1 ..o.5..o. | * * 5 * | 0 0 2 0 0 2 2 0 0 | 0 0 1 0 0 2 2 0 1 2 1 0 | 0 0 1 1 2 1 ...o5...o | * * * 10 | 0 0 0 1 0 0 1 1 1 | 0 0 0 1 1 0 1 0 0 1 1 1 | 0 1 0 1 1 1 --------------+----------+-----------------------+---------------------------+------------ x... .... | 2 0 0 0 | 5 * * * * * * * * | 1 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0 oo..5oo..&#x | 1 1 0 0 | * 5 * * * * * * * | 0 2 0 0 0 2 0 0 0 0 0 0 | 1 0 2 0 1 0 o.o.5o.o.&#x | 1 0 1 0 | * * 10 * * * * * * | 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0 o..o5o..o&#x | 1 0 0 1 | * * * 10 * * * * * | 0 0 0 1 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0 .x.. .... | 0 2 0 0 | * * * * 5 * * * * | 0 1 0 0 0 0 0 1 1 0 0 0 | 1 0 1 0 0 1 .oo.5.oo.&#x | 0 1 1 0 | * * * * * 10 * * * | 0 0 0 0 0 1 0 0 1 1 0 0 | 0 0 1 0 1 1 ..oo5..oo&#x | 0 0 1 1 | * * * * * * 10 * * | 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 1 1 ...x .... | 0 0 0 2 | * * * * * * * 5 * | 0 0 0 1 0 0 0 0 0 0 1 1 | 0 1 0 1 0 1 .... ...x | 0 0 0 2 | * * * * * * * * 5 | 0 0 0 0 1 0 0 0 0 1 0 1 | 0 1 0 0 1 1 --------------+----------+-----------------------+---------------------------+------------ x...5o... | 5 0 0 0 | 5 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * | 1 1 0 0 0 0 xx.. ....&#x | 2 2 0 0 | 1 2 0 0 1 0 0 0 0 | * 5 * * * * * * * * * * | 1 0 1 0 0 0 x.o. ....&#x | 2 0 1 0 | 1 0 2 0 0 0 0 0 0 | * * 5 * * * * * * * * * | 0 0 1 1 0 0 x..x ....&#x | 2 0 0 2 | 1 0 0 2 0 0 0 1 0 | * * * 5 * * * * * * * * | 0 1 0 1 0 0 .... o..x&#x | 1 0 0 2 | 0 0 0 2 0 0 0 0 1 | * * * * 5 * * * * * * * | 0 1 0 0 1 0 ooo.5ooo.&#x | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 | * * * * * 10 * * * * * * | 0 0 1 0 1 0 o.oo5o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 1 0 0 | * * * * * * 10 * * * * * | 0 0 0 1 1 0 .x..5.o.. | 0 5 0 0 | 0 0 0 0 5 0 0 0 0 | * * * * * * * 1 * * * * | 1 0 0 0 0 1 .xo. ....&#x | 0 2 1 0 | 0 0 0 0 1 2 0 0 0 | * * * * * * * * 5 * * * | 0 0 1 0 0 1 .... .ofx&#xt | 0 1 2 2 | 0 0 0 0 0 2 2 0 1 | * * * * * * * * * 5 * * | 0 0 0 0 1 1 ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * 5 * | 0 0 0 1 0 1 ...x5...x | 0 0 0 10 | 0 0 0 0 0 0 0 5 5 | * * * * * * * * * * * 1 | 0 1 0 0 0 1 --------------+----------+-----------------------+---------------------------+------------ xx..5oo..&#x ♦ 5 5 0 0 | 5 5 0 0 5 0 0 0 0 | 1 5 0 0 0 0 0 1 0 0 0 0 | 1 * * * * * x..x5o..x&#x ♦ 5 0 0 10 | 5 0 0 10 0 0 0 5 5 | 1 0 0 5 5 0 0 0 0 0 0 1 | * 1 * * * * xxo. ....&#x ♦ 2 2 1 0 | 1 2 2 0 1 2 0 0 0 | 0 1 1 0 0 2 0 0 1 0 0 0 | * * 5 * * * x.ox ....&#x ♦ 2 0 1 2 | 1 0 2 2 0 0 2 1 0 | 0 0 1 1 0 0 2 0 0 0 1 0 | * * * 5 * * .... oofx&#xr ♦ 1 1 2 2 | 0 1 2 2 0 2 2 0 1 | 0 0 0 0 1 2 2 0 0 1 0 0 | * * * * 5 * .xox5.ofx&#xt ♦ 0 5 5 10 | 0 0 0 0 5 10 10 5 5 | 0 0 0 0 0 0 0 1 5 5 5 1 | * * * * * 1
{5} || pero → height = (sqrt(5)-1)/4 = 0.309017
o...5o... | 5 * * * | 2 1 2 2 0 0 0 0 0 | 1 2 2 2 1 2 2 0 0 0 0 0 | 1 1 2 2 1 0
.o..5.o.. | * 5 * * | 0 1 0 0 2 2 0 0 0 | 0 2 0 0 0 2 0 1 2 1 0 0 | 1 0 2 0 1 1
..o.5..o. | * * 5 * | 0 0 2 0 0 2 2 0 0 | 0 0 1 0 0 2 2 0 1 2 1 0 | 0 0 1 1 2 1
...o5...o | * * * 10 | 0 0 0 1 0 0 1 1 1 | 0 0 0 1 1 0 1 0 0 1 1 1 | 0 1 0 1 1 1
--------------+----------+-----------------------+---------------------------+------------
x... .... | 2 0 0 0 | 5 * * * * * * * * | 1 1 1 1 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0
oo..5oo..&#x | 1 1 0 0 | * 5 * * * * * * * | 0 2 0 0 0 2 0 0 0 0 0 0 | 1 0 2 0 1 0
o.o.5o.o.&#x | 1 0 1 0 | * * 10 * * * * * * | 0 0 1 0 0 1 1 0 0 0 0 0 | 0 0 1 1 1 0
o..o5o..o&#x | 1 0 0 1 | * * * 10 * * * * * | 0 0 0 1 1 0 1 0 0 0 0 0 | 0 1 0 1 1 0
.x.. .... | 0 2 0 0 | * * * * 5 * * * * | 0 1 0 0 0 0 0 1 1 0 0 0 | 1 0 1 0 0 1
.oo.5.oo.&#x | 0 1 1 0 | * * * * * 10 * * * | 0 0 0 0 0 1 0 0 1 1 0 0 | 0 0 1 0 1 1
..oo5..oo&#x | 0 0 1 1 | * * * * * * 10 * * | 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 1 1
...x .... | 0 0 0 2 | * * * * * * * 5 * | 0 0 0 1 0 0 0 0 0 0 1 1 | 0 1 0 1 0 1
.... ...x | 0 0 0 2 | * * * * * * * * 5 | 0 0 0 0 1 0 0 0 0 1 0 1 | 0 1 0 0 1 1
--------------+----------+-----------------------+---------------------------+------------
x...5o... | 5 0 0 0 | 5 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * | 1 1 0 0 0 0
xx.. ....&#x | 2 2 0 0 | 1 2 0 0 1 0 0 0 0 | * 5 * * * * * * * * * * | 1 0 1 0 0 0
x.o. ....&#x | 2 0 1 0 | 1 0 2 0 0 0 0 0 0 | * * 5 * * * * * * * * * | 0 0 1 1 0 0
x..x ....&#x | 2 0 0 2 | 1 0 0 2 0 0 0 1 0 | * * * 5 * * * * * * * * | 0 1 0 1 0 0
.... o..x&#x | 1 0 0 2 | 0 0 0 2 0 0 0 0 1 | * * * * 5 * * * * * * * | 0 1 0 0 1 0
ooo.5ooo.&#x | 1 1 1 0 | 0 1 1 0 0 1 0 0 0 | * * * * * 10 * * * * * * | 0 0 1 0 1 0
o.oo5o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 1 0 0 | * * * * * * 10 * * * * * | 0 0 0 1 1 0
.x..5.o.. | 0 5 0 0 | 0 0 0 0 5 0 0 0 0 | * * * * * * * 1 * * * * | 1 0 0 0 0 1
.xo. ....&#x | 0 2 1 0 | 0 0 0 0 1 2 0 0 0 | * * * * * * * * 5 * * * | 0 0 1 0 0 1
.... .ofx&#xt | 0 1 2 2 | 0 0 0 0 0 2 2 0 1 | * * * * * * * * * 5 * * | 0 0 0 0 1 1
..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 0 | * * * * * * * * * * 5 * | 0 0 0 1 0 1
...x5...x | 0 0 0 10 | 0 0 0 0 0 0 0 5 5 | * * * * * * * * * * * 1 | 0 1 0 0 0 1
--------------+----------+-----------------------+---------------------------+------------
xx..5oo..&#x ♦ 5 5 0 0 | 5 5 0 0 5 0 0 0 0 | 1 5 0 0 0 0 0 1 0 0 0 0 | 1 * * * * *
x..x5o..x&#x ♦ 5 0 0 10 | 5 0 0 10 0 0 0 5 5 | 1 0 0 5 5 0 0 0 0 0 0 1 | * 1 * * * *
xxo. ....&#x ♦ 2 2 1 0 | 1 2 2 0 1 2 0 0 0 | 0 1 1 0 0 2 0 0 1 0 0 0 | * * 5 * * *
x.ox ....&#x ♦ 2 0 1 2 | 1 0 2 2 0 0 2 1 0 | 0 0 1 1 0 0 2 0 0 0 1 0 | * * * 5 * *
.... oofx&#xr ♦ 1 1 2 2 | 0 1 2 2 0 2 2 0 1 | 0 0 0 0 1 2 2 0 0 1 0 0 | * * * * 5 *
.xox5.ofx&#xt ♦ 0 5 5 10 | 0 0 0 0 5 10 10 5 5 | 0 0 0 0 0 0 0 1 5 5 5 1 | * * * * * 1
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