Acronym ..., K-4.146 Name pentagon - pentagonal-rotunda wedge,{5} || pero Segmentochoron display Circumradius sqrt[5+2 sqrt(5)] = 3.077684 Confer related segmentochora: ike || id   peppia pero   related CRFs: {5} || pocuro   general polytopal classes: segmentochora

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
```

 © 2004-2021 top of page