| Acronym | penu |
| Name |
pentachoron-based ursateron, pen-based ursulate, vertex figure of o3o3o3o4s3s |
| Circumradius | sqrt[2+sqrt(5)]/2 = 1.029086 |
|
Inradius wrt. pen | sqrt[(1+3 sqrt(5))/12] = 0.801468 |
|
Inradius wrt. rap | sqrt[(5 sqrt(5)-2)/20] = 0.677508 |
|
Inradius wrt. tetu | sqrt[sqrt(5)-2]/2 = 0.242934 |
| Volume | [11 sqrt(5 sqrt(5)-2)+2 sqrt(15+45 sqrt(5))+(140+65 sqrt(5)) sqrt(sqrt(5)-2)]/960 = 0.201536 |
| Surface | [70+41 sqrt(5)]/48 = 3.368308 |
| Face vector | 20, 65, 80, 45, 12 |
| Confer |
|
Incidence matrix according to Dynkin symbol
ofx3xoo3ooo3ooo&#xt → height(1,2) = sqrt[(1+sqrt(5))/10] = 0.568864
height(2,3) = sqrt[(2+sqrt(5))/5] = 0.920442
(rap || pseudo f-pen || pen)
o..3o..3o..3o.. | 10 * * | 6 2 0 0 | 3 6 1 6 0 | 3 2 3 6 0 | 1 3 2 0
.o.3.o.3.o.3.o. | * 5 * | 0 4 1 0 | 0 0 4 6 0 | 0 0 6 4 0 | 0 4 1 0
..o3..o3..o3..o | * * 5 | 0 0 1 4 | 0 0 4 0 6 | 0 0 6 0 4 | 0 4 0 1
--------------------+--------+------------+----------------+-------------+--------
... x.. ... ... | 2 0 0 | 30 * * * | 1 2 0 1 0 | 2 1 1 2 0 | 1 2 1 0
oo.3oo.3oo.3oo.&#x | 1 1 0 | * 20 * * | 0 0 1 3 0 | 0 0 3 3 0 | 0 3 1 0
.oo3.oo3.oo3.oo&#x | 0 1 1 | * * 5 * ♦ 0 0 4 0 0 | 0 0 6 0 0 | 0 4 0 0
..x ... ... ... | 0 0 2 | * * * 10 | 0 0 1 0 3 | 0 0 3 0 3 | 0 3 0 1
--------------------+--------+------------+----------------+-------------+--------
o..3x.. ... ... | 3 0 0 | 3 0 0 0 | 10 * * * * | 2 0 1 0 0 | 1 2 0 0
... x..3o.. ... | 3 0 0 | 3 0 0 0 | * 20 * * * | 1 1 0 1 0 | 1 1 1 0
ofx ... ... ...&#xt | 1 2 2 | 0 2 2 1 | * * 10 * * | 0 0 3 0 0 | 0 3 0 0
... xo. ... ...&#x | 2 1 0 | 1 2 0 0 | * * * 30 * | 0 0 1 2 0 | 0 2 1 0
..x3..o ... ... | 0 0 3 | 0 0 0 3 | * * * * 10 | 0 0 1 0 2 | 0 2 0 1
--------------------+--------+------------+----------------+-------------+--------
o..3x..3o.. ... ♦ 6 0 0 | 12 0 0 0 | 4 4 0 0 0 | 5 * * * * | 1 1 0 0
... x..3o..3o.. ♦ 4 0 0 | 6 0 0 0 | 0 4 0 0 0 | * 5 * * * | 1 0 1 0
ofx3xoo ... ...&#xt ♦ 3 3 3 | 3 6 3 3 | 1 0 3 3 1 | * * 10 * * | 0 2 0 0
... xo.3oo. ...&#x ♦ 3 1 0 | 3 3 0 0 | 0 1 0 3 0 | * * * 20 * | 0 1 1 0
..x3..o3..o ... ♦ 0 0 4 | 0 0 0 6 | 0 0 0 0 4 | * * * * 5 | 0 1 0 1
--------------------+--------+------------+----------------+-------------+--------
o..3x..3o..3o.. ♦ 10 0 0 | 30 0 0 0 | 10 20 0 0 0 | 5 5 0 0 0 | 1 * * *
ofx3xoo3ooo ...&#xt ♦ 6 4 4 | 12 12 4 6 | 4 4 6 12 4 | 1 0 4 4 1 | * 5 * *
... xo.3oo.3oo.&#x ♦ 4 1 0 | 6 4 0 0 | 0 4 0 6 0 | 0 1 0 4 0 | * * 5 *
..x3..o3..o3..o ♦ 0 0 5 | 0 0 0 10 | 0 0 0 0 10 | 0 0 0 0 5 | * * * 1
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