Acronym | rappy |
Name |
rectified-pentachoric pyramid, vertex cap of hin |
Circumradius | sqrt(5/8) = 0.790569 |
Inradius wrt. pen | 3/sqrt(40) = 0.474342 |
Inradius wrt. octpy | 1/sqrt(8) = 0.353553 |
Inradius wrt. rap | -1/sqrt(40) = -0.158114 |
Lace city in approx. ASCII-art |
O o o = o3o3o O = o3x3o T T = x3o3o |
Volume | 11 sqrt(2)/480 = 0.032409 |
Dihedral angles
(at margins) | |
Face vector | 11, 40, 60, 40, 11 |
Confer |
|
Incidence matrix according to Dynkin symbol
oo3ox3oo3oo&#x → height = sqrt(2/5) = 0.632456
(pt || rap)
o.3o.3o.3o. | 1 * ♦ 10 0 | 30 0 0 | 10 20 0 0 | 5 5 0
.o3.o3.o3.o | * 10 ♦ 1 6 | 6 3 6 | 3 6 3 2 | 3 2 1
---------------+------+-------+----------+-----------+------
oo3oo3oo3oo&#x | 1 1 | 10 * ♦ 6 0 0 | 3 6 0 0 | 3 2 0
.. .x .. .. | 0 2 | * 30 | 1 1 2 | 1 2 2 1 | 2 1 1
---------------+------+-------+----------+-----------+------
.. ox .. ..&#x | 1 2 | 2 1 | 30 * * | 1 2 0 0 | 2 1 0
.o3.x .. .. | 0 3 | 0 3 | * 10 * | 1 0 2 0 | 2 0 1
.. .x3.o .. | 0 3 | 0 3 | * * 20 | 0 1 1 1 | 1 1 1
---------------+------+-------+----------+-----------+------
oo3ox .. ..&#x ♦ 1 3 | 3 3 | 3 1 0 | 10 * * * | 2 0 0
.. ox3oo ..&#x ♦ 1 3 | 3 3 | 3 0 1 | * 20 * * | 1 1 0
.o3.x3.o .. ♦ 0 6 | 0 12 | 0 4 4 | * * 5 * | 1 0 1
.. .x3.o3.o ♦ 0 4 | 0 6 | 0 0 4 | * * * 5 | 0 1 1
---------------+------+-------+----------+-----------+------
oo3ox3oo ..&#x ♦ 1 6 | 6 12 | 12 4 4 | 4 4 1 0 | 5 * *
.. ox3oo3oo&#x ♦ 1 4 | 4 6 | 6 0 4 | 0 4 0 1 | * 5 *
.o3.x3.o3.o ♦ 0 10 | 0 30 | 0 10 20 | 0 0 5 5 | * * 1
oxo3oox3ooo&#x → height(1,2) = height(2,3) = sqrt(5/8) = 0.790569 height(1,3) = 1/sqrt(2) = 0.707107 o..3o..3o.. | 1 * * ♦ 4 6 0 0 0 | 6 12 12 0 0 0 0 0 | 4 4 4 6 12 0 0 0 0 | 1 1 4 4 0 .o.3.o.3.o. | * 4 * ♦ 1 0 3 3 0 | 3 0 3 3 3 3 0 0 | 3 0 0 3 3 1 3 1 0 | 1 0 3 1 1 ..o3..o3..o | * * 6 ♦ 0 1 0 2 4 | 0 4 2 0 1 4 2 2 | 0 2 2 1 4 0 2 2 1 | 0 1 2 2 1 ---------------+-------+-------------+--------------------+--------------------+---------- oo.3oo.3oo.&#x | 1 1 0 | 4 * * * * ♦ 3 0 3 0 0 0 0 0 | 3 0 0 3 3 0 0 0 0 | 1 0 3 1 0 o.o3o.o3o.o&#x | 1 0 1 | * 6 * * * ♦ 0 4 2 0 0 0 0 0 | 0 2 2 1 4 0 0 0 0 | 0 1 2 2 0 .x. ... ... | 0 2 0 | * * 6 * * | 1 0 0 2 1 0 0 0 | 2 0 0 1 0 1 2 0 0 | 1 0 2 0 1 .oo3.oo3.oo&#x | 0 1 1 | * * * 12 * | 0 0 1 0 1 2 0 0 | 0 0 0 1 2 0 2 1 0 | 0 0 2 1 1 ... ..x ... | 0 0 2 | * * * * 12 | 0 1 0 0 0 1 1 1 | 0 1 1 0 1 0 1 1 1 | 0 1 1 1 1 ---------------+-------+-------------+--------------------+--------------------+---------- ox. ... ...&#x | 1 2 0 | 2 0 1 0 0 | 6 * * * * * * * | 2 0 0 1 0 0 0 0 0 | 1 0 2 0 0 ... o.x ...&#x | 1 0 2 | 0 2 0 0 1 | * 12 * * * * * * | 0 1 1 0 1 0 0 0 0 | 0 1 1 1 0 ooo3ooo3ooo&#x | 1 1 1 | 1 1 0 1 0 | * * 12 * * * * * | 0 0 0 1 2 0 0 0 0 | 0 0 2 1 0 .x.3.o. ... | 0 3 0 | 0 0 3 0 0 | * * * 4 * * * * | 1 0 0 0 0 1 1 0 0 | 1 0 1 0 1 .xo ... ...&#x | 0 2 1 | 0 0 1 2 0 | * * * * 6 * * * | 0 0 0 1 0 0 2 0 0 | 0 0 2 0 1 ... .ox ...&#x | 0 1 2 | 0 0 0 2 1 | * * * * * 12 * * | 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1 ..o3..x ... | 0 0 3 | 0 0 0 0 3 | * * * * * * 4 * | 0 1 0 0 0 0 1 0 1 | 0 1 1 0 1 ... ..x3..o | 0 0 3 | 0 0 0 0 3 | * * * * * * * 4 | 0 0 1 0 0 0 0 1 1 | 0 1 0 1 1 ---------------+-------+-------------+--------------------+--------------------+---------- ox.3oo. ...&#x ♦ 1 3 0 | 3 0 3 0 0 | 3 0 0 1 0 0 0 0 | 4 * * * * * * * * | 1 0 1 0 0 o.o3o.x ...&#x ♦ 1 0 3 | 0 3 0 0 3 | 0 3 0 0 0 0 1 0 | * 4 * * * * * * * | 0 1 1 0 0 ... o.x3o.o&#x ♦ 1 0 3 | 0 3 0 0 3 | 0 3 0 0 0 0 0 1 | * * 4 * * * * * * | 0 1 0 1 0 oxo ... ...&#x ♦ 1 2 1 | 2 1 1 2 0 | 1 0 2 0 1 0 0 0 | * * * 6 * * * * * | 0 0 2 0 0 ... oox ...&#x ♦ 1 1 2 | 1 2 0 2 1 | 0 1 2 0 0 1 0 0 | * * * * 12 * * * * | 0 0 1 1 0 .x.3.o.3.o. ♦ 0 4 0 | 0 0 6 0 0 | 0 0 0 4 0 0 0 0 | * * * * * 1 * * * | 1 0 0 0 1 .xo3.ox ...&#x ♦ 0 3 3 | 0 0 3 6 3 | 0 0 0 1 3 3 1 0 | * * * * * * 4 * * | 0 0 1 0 1 ... .ox3.oo&#x ♦ 0 1 3 | 0 0 0 3 3 | 0 0 0 0 0 3 0 1 | * * * * * * * 4 * | 0 0 0 1 1 ..o3..x3..o ♦ 0 0 6 | 0 0 0 0 12 | 0 0 0 0 0 0 4 4 | * * * * * * * * 1 | 0 1 0 0 1 ---------------+-------+-------------+--------------------+--------------------+---------- ox.3oo.3oo.&#x ♦ 1 4 0 | 4 0 6 0 0 | 6 0 0 4 0 0 0 0 | 4 0 0 0 0 1 0 0 0 | 1 * * * * o.o3o.x3o.o&#x ♦ 1 0 6 | 0 6 0 0 12 | 0 12 0 0 0 0 4 4 | 0 4 4 0 0 0 0 0 1 | * 1 * * * oxo3oox ...&#x ♦ 1 3 3 | 3 3 3 6 3 | 3 3 6 1 3 3 1 0 | 1 1 0 3 3 0 1 0 0 | * * 4 * * ... oox3ooo&#x ♦ 1 1 3 | 1 3 0 3 3 | 0 3 3 0 0 3 0 1 | 0 0 1 0 3 0 0 1 0 | * * * 4 * .xo3.ox3.oo&#x ♦ 0 4 6 | 0 0 6 12 12 | 0 0 0 4 6 12 4 4 | 0 0 0 0 0 1 4 4 1 | * * * * 1
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