Acronym | poct |
Name | pentagon - octahedron duoprism |
Circumradius | sqrt[(10+sqrt(5))/10] = 1.106168 |
Volume | sqrt[50+20 sqrt(5)]/12 = 0.811041 |
Face vector | 30, 90, 106, 57, 13 |
Confer |
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External links |
As abstract polytope poct is isomorphic to stoct, thereby replacing pentagons by pentagrams, resp. pip by stip, resp. trapedip by tistadip.
Incidence matrix according to Dynkin symbol
x5o x3o4o . . . . . | 30 | 2 4 | 1 8 4 | 4 8 1 | 4 2 ----------+----+-------+---------+---------+---- x . . . . | 2 | 30 * | 1 4 0 | 4 4 0 | 4 1 . . x . . | 2 | * 60 | 0 2 2 | 1 4 1 | 2 2 ----------+----+-------+---------+---------+---- x5o . . . | 5 | 5 0 | 6 * * | 4 0 0 | 4 0 x . x . . | 4 | 2 2 | * 60 * | 1 2 0 | 2 1 . . x3o . | 3 | 0 3 | * * 40 | 0 2 1 | 1 2 ----------+----+-------+---------+---------+---- x5o x . . ♦ 10 | 10 5 | 2 5 0 | 12 * * | 2 0 x . x3o . ♦ 6 | 3 6 | 0 3 2 | * 40 * | 1 1 . . x3o4o ♦ 6 | 0 12 | 0 0 8 | * * 5 | 0 2 ----------+----+-------+---------+---------+---- x5o x3o . ♦ 15 | 15 15 | 3 15 5 | 3 5 0 | 8 * x . x3o4o ♦ 12 | 6 24 | 0 12 16 | 0 8 2 | * 5
x5o o3x3o . . . . . | 30 | 2 4 | 1 8 2 2 | 4 4 4 1 | 2 2 2 ----------+----+-------+------------+------------+------ x . . . . | 2 | 30 * | 1 4 0 0 | 4 2 2 0 | 2 2 1 . . . x . | 2 | * 60 | 0 2 1 1 | 1 2 2 1 | 1 1 2 ----------+----+-------+------------+------------+------ x5o . . . | 5 | 5 0 | 6 * * * | 4 0 0 0 | 2 2 0 x . . x . | 4 | 2 2 | * 60 * * | 1 1 1 0 | 1 1 1 . . o3x . | 3 | 0 3 | * * 20 * | 0 2 0 1 | 1 0 2 . . . x3o | 3 | 0 3 | * * * 20 | 0 0 2 1 | 0 1 2 ----------+----+-------+------------+------------+------ x5o . x . ♦ 10 | 10 5 | 2 5 0 0 | 12 * * * | 1 1 0 x . o3x . ♦ 6 | 3 6 | 0 3 2 0 | * 20 * * | 1 0 1 x . . x3o ♦ 6 | 3 6 | 0 3 0 2 | * * 20 * | 0 1 1 . . o3x3o ♦ 6 | 0 12 | 0 0 4 4 | * * * 5 | 0 0 2 ----------+----+-------+------------+------------+------ x5o o3x . ♦ 15 | 15 15 | 3 15 5 0 | 3 5 0 0 | 4 * * x5o . x3o ♦ 15 | 15 15 | 3 15 0 5 | 3 0 5 0 | * 4 * x . o3x3o ♦ 12 | 6 24 | 0 12 8 8 | 0 4 4 2 | * * 5
xo3ox xx5oo&#x → height = sqrt(2/3) = 0.816497
(trapedip || {3}-gyro trapedip)
o.3o. o.5o. | 15 * | 2 2 2 0 0 | 1 4 1 2 1 4 0 0 0 | 2 2 1 4 2 2 0 0 | 1 2 2 1 0
.o3.o .o5.o | * 15 | 0 0 2 2 2 | 0 0 0 1 2 4 1 4 1 | 0 0 1 2 4 2 2 2 | 0 2 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x. .. .. .. | 2 0 | 15 * * * * | 1 2 0 1 0 0 0 0 0 | 2 1 1 2 0 0 0 0 | 1 2 1 0 0
.. .. x. .. | 2 0 | * 15 * * * | 0 2 1 0 0 2 0 0 0 | 1 2 0 2 1 2 0 0 | 1 2 2 1 0
oo3oo oo5oo&#x | 1 1 | * * 30 * * | 0 0 0 1 1 2 0 0 0 | 0 0 1 2 2 1 0 0 | 0 1 1 1 0
.. .x .. .. | 0 2 | * * * 15 * | 0 0 0 0 1 0 1 2 0 | 0 0 1 0 2 0 2 1 | 0 2 0 1 1
.. .. .x .. | 0 2 | * * * * 15 | 0 0 0 0 0 2 0 2 1 | 0 0 0 1 2 2 1 2 | 0 2 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. .. .. | 3 0 | 3 0 0 0 0 | 5 * * * * * * * * | 2 0 1 0 0 0 0 0 | 1 2 0 0 0
x. .. x. .. | 4 0 | 2 2 0 0 0 | * 15 * * * * * * * | 1 1 0 1 0 0 0 0 | 1 1 1 0 0
.. .. x.5o. | 5 0 | 0 5 0 0 0 | * * 3 * * * * * * | 0 2 0 0 0 2 0 0 | 1 0 2 1 0
xo .. .. ..&#x | 2 1 | 1 0 2 0 0 | * * * 15 * * * * * | 0 0 1 2 0 0 0 0 | 0 2 1 0 0
.. ox .. ..&#x | 1 2 | 0 0 2 1 0 | * * * * 15 * * * * | 0 0 1 0 2 0 0 0 | 0 2 0 1 0
.. .. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * * * 30 * * * | 0 0 0 1 1 1 0 0 | 0 1 1 1 0
.o3.x .. .. | 0 3 | 0 0 0 3 0 | * * * * * * 5 * * | 0 0 1 0 0 0 2 0 | 0 2 0 0 1
.. .x .x .. | 0 4 | 0 0 0 2 2 | * * * * * * * 15 * | 0 0 0 0 1 0 1 1 | 0 1 0 1 1
.. .. .x5.o | 0 5 | 0 0 0 0 5 | * * * * * * * * 3 | 0 0 0 0 0 2 0 2 | 0 0 1 2 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x. .. ♦ 6 0 | 6 3 0 0 0 | 2 3 0 0 0 0 0 0 0 | 5 * * * * * * * | 1 1 0 0 0
x. .. x.5o. ♦ 10 0 | 5 10 0 0 0 | 0 5 2 0 0 0 0 0 0 | * 3 * * * * * * | 1 0 1 0 0
xo3ox .. ..&#x ♦ 3 3 | 3 0 6 3 0 | 1 0 0 3 3 0 1 0 0 | * * 5 * * * * * | 0 2 0 0 0
xo .. xx ..&#x ♦ 4 2 | 2 2 4 0 1 | 0 1 0 2 0 2 0 0 0 | * * * 15 * * * * | 0 1 1 0 0
.. ox xx ..&#x ♦ 2 4 | 0 1 4 2 2 | 0 0 0 0 2 2 0 1 0 | * * * * 15 * * * | 0 1 0 1 0
.. .. xx5oo&#x ♦ 5 5 | 0 5 5 0 5 | 0 0 1 0 0 5 0 0 1 | * * * * * 6 * * | 0 0 1 1 0
.o3.x .x .. ♦ 0 6 | 0 0 0 6 3 | 0 0 0 0 0 0 2 3 0 | * * * * * * 5 * | 0 1 0 0 1
.. .x .x5.o ♦ 0 10 | 0 0 0 5 10 | 0 0 0 0 0 0 0 5 2 | * * * * * * * 3 | 0 0 0 1 1
---------------+-------+----------------+------------------------+-------------------+----------
x.3o. x.5o. ♦ 15 0 | 15 15 0 0 0 | 5 15 3 0 0 0 0 0 0 | 5 3 0 0 0 0 0 0 | 1 * * * *
xo3ox xx ..&#x ♦ 6 6 | 6 6 6 6 6 | 2 3 0 6 6 6 2 3 0 | 1 0 2 3 3 0 1 0 | * 5 * * *
xo .. xx5oo&#x ♦ 10 5 | 5 10 10 0 5 | 0 5 2 5 0 10 0 0 1 | 0 1 0 5 0 2 0 0 | * * 3 * *
.. ox xx5oo&#x ♦ 5 10 | 0 5 10 5 10 | 0 0 1 0 5 10 0 5 2 | 0 0 0 0 5 2 0 1 | * * * 3 *
.o3.x .x5.o ♦ 0 15 | 0 0 0 15 15 | 0 0 0 0 0 0 5 15 3 | 0 0 0 0 0 0 5 3 | * * * * 1
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