Acronym | cubpy, K-4.26 |
Name |
cubical pyramid, vertex-pyramid of ico |
|,>,O device | line prism prism pyramid = |||> |
© | |
Segmentochoron display | |
Circumradius | 1 |
Volume | 1/8 = 0.125 |
Dihedral angles | |
Face vector | 9, 20, 18, 7 |
Confer |
|
External links |
Incidence matrix according to Dynkin symbol
oo3oo4ox&#x → height = 1/2
(pt || cube)
o.3o.4o. | 1 * ♦ 8 0 | 12 0 | 6 0
.o3.o4.o | * 8 | 1 3 | 3 3 | 3 1
------------+-----+------+------+----
oo3oo4oo&#x | 1 1 | 8 * | 3 0 | 3 0
.. .. .x | 0 2 | * 12 | 1 2 | 2 1
------------+-----+------+------+----
.. .. ox&#x | 1 2 | 2 1 | 12 * | 2 0
.. .o4.x | 0 4 | 0 4 | * 6 | 1 1
------------+-----+------+------+----
.. oo4ox&#x ♦ 1 4 | 4 4 | 4 1 | 6 *
.o3.o4.x ♦ 0 8 | 0 12 | 0 6 | * 1
ox ox4oo&#x → height = 1/2
(pt || cube)
o. o.4o. | 1 * ♦ 8 0 0 | 4 8 0 0 | 4 2 0
.o .o4.o | * 8 | 1 1 2 | 1 2 2 1 | 2 1 1
------------+-----+-------+---------+------
oo oo4oo&#x | 1 1 | 8 * * | 1 2 0 0 | 2 1 0
.x .. .. | 0 2 | * 4 * | 1 0 2 0 | 2 0 1
.. .x .. | 0 2 | * * 8 | 0 1 1 1 | 1 1 1
------------+-----+-------+---------+------
ox .. ..&#x | 1 2 | 2 1 0 | 4 * * * | 2 0 0
.. ox ..&#x | 1 2 | 2 0 1 | * 8 * * | 1 1 0
.x .x .. | 0 4 | 0 2 2 | * * 4 * | 1 0 1
.. .x4.o | 0 4 | 0 0 4 | * * * 2 | 0 1 1
------------+-----+-------+---------+------
ox ox ..&#x ♦ 1 4 | 4 2 2 | 2 2 1 0 | 4 * *
.. ox4oo&#x ♦ 1 4 | 4 0 4 | 0 4 0 1 | * 2 *
.x .x4.o ♦ 0 8 | 0 4 8 | 0 0 4 2 | * * 1
oxx4ooo&#x → height(1,2) = height(1,3) = 1/sqrt(2) = 0.707107 height(2,3) = 1 o..4o.. | 1 * * ♦ 4 4 0 0 0 | 4 4 4 0 0 0 | 1 1 4 0 .o.4.o. | * 4 * | 1 0 2 1 0 | 2 0 1 1 2 0 | 1 0 2 1 ..o4..o | * * 4 | 0 1 0 1 2 | 0 2 1 0 2 1 | 0 1 2 1 -----------+-------+-----------+-------------+-------- oo.4oo.&#x | 1 1 0 | 4 * * * * | 2 0 1 0 0 0 | 1 0 2 0 o.o4o.o&#x | 1 0 1 | * 4 * * * | 0 2 1 0 0 0 | 0 1 2 0 .x. ... | 0 2 0 | * * 4 * * | 1 0 0 1 1 0 | 1 0 1 1 .oo4.oo&#x | 0 1 1 | * * * 4 * | 0 0 1 0 2 0 | 0 0 2 1 ..x ... | 0 0 2 | * * * * 4 | 0 1 0 0 1 1 | 0 1 1 1 -----------+-------+-----------+-------------+-------- ox. ...&#x | 1 2 0 | 2 0 1 0 0 | 4 * * * * * | 1 0 1 0 o.x ...&#x | 1 0 2 | 0 2 0 0 1 | * 4 * * * * | 0 1 1 0 ooo4ooo&#x | 1 1 1 | 1 1 0 1 0 | * * 4 * * * | 0 0 2 0 .x.4.o. | 0 4 0 | 0 0 4 0 0 | * * * 1 * * | 1 0 0 1 .xx ...&#x | 0 2 2 | 0 0 1 2 1 | * * * * 4 * | 0 0 1 1 ..x4..o | 0 0 4 | 0 0 0 0 4 | * * * * * 1 | 0 1 0 1 -----------+-------+-----------+-------------+-------- ox.4oo.&#x ♦ 1 4 0 | 4 0 4 0 0 | 4 0 0 1 0 0 | 1 * * * o.x4o.o&#x ♦ 1 0 4 | 0 4 0 0 4 | 0 4 0 0 0 1 | * 1 * * oxx ...&#x ♦ 1 2 2 | 2 2 1 2 1 | 1 1 2 0 1 0 | * * 4 * .xx4.oo&#x ♦ 0 4 4 | 0 0 4 4 4 | 0 0 0 1 4 1 | * * * 1
or o..4o.. | 1 * ♦ 8 0 0 | 8 4 0 0 | 2 4 0 .o.4.o. & | * 8 | 1 2 1 | 2 1 1 2 | 1 2 1 -------------+-----+-------+---------+------ oo.4oo.&#x & | 1 1 | 8 * * | 2 1 0 0 | 1 2 0 .x. ... & | 0 2 | * 8 * | 1 0 1 1 | 1 1 1 .oo4.oo&#x | 0 2 | * * 4 | 0 1 0 2 | 0 2 1 -------------+-----+-------+---------+------ ox. ...&#x & | 1 2 | 2 1 0 | 8 * * * | 1 1 0 ooo4ooo&#x | 1 2 | 2 0 1 | * 4 * * | 0 2 0 .x.4.o. & | 0 4 | 0 4 0 | * * 2 * | 1 0 1 .xx ...&#x | 0 4 | 0 2 2 | * * * 4 | 0 1 1 -------------+-----+-------+---------+------ ox.4oo.&#x & ♦ 1 4 | 4 4 0 | 4 0 1 0 | 2 * * oxx ...&#x ♦ 1 4 | 4 2 2 | 2 2 0 1 | * 4 * .xx4.oo&#x ♦ 0 8 | 0 8 4 | 0 0 2 4 | * * 1
oxx oxx&#x → height(1,2) = height(1,3) = 1/sqrt(2) = 0.707107 height(2,3) = 1 o.. o.. | 1 * * ♦ 4 4 0 0 0 0 0 | 2 2 2 2 4 0 0 0 0 | 1 1 2 2 0 .o. .o. | * 4 * | 1 0 1 1 1 0 0 | 1 1 0 0 1 1 1 1 0 | 1 0 1 1 1 ..o ..o | * * 4 | 0 1 0 0 1 1 1 | 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1 -----------+-------+---------------+-------------------+---------- oo. oo.&#x | 1 1 0 | 4 * * * * * * | 1 1 0 0 1 0 0 0 0 | 1 0 1 1 0 o.o o.o&#x | 1 0 1 | * 4 * * * * * | 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 .x. ... | 0 2 0 | * * 2 * * * * | 1 0 0 0 0 1 1 0 0 | 1 0 1 0 1 ... .x. | 0 2 0 | * * * 2 * * * | 0 1 0 0 0 1 0 1 0 | 1 0 0 1 1 .oo .oo&#x | 0 1 1 | * * * * 4 * * | 0 0 0 0 1 0 1 1 0 | 0 0 1 1 1 ..x ... | 0 0 2 | * * * * * 2 * | 0 0 1 0 0 0 1 0 1 | 0 1 1 0 1 ... ..x | 0 0 2 | * * * * * * 2 | 0 0 0 1 0 0 0 1 1 | 0 1 0 1 1 -----------+-------+---------------+-------------------+---------- ox. ...&#x | 1 2 0 | 2 0 1 0 0 0 0 | 2 * * * * * * * * | 1 0 1 0 0 ... ox.&#x | 1 2 0 | 2 0 0 1 0 0 0 | * 2 * * * * * * * | 1 0 0 1 0 o.x ...&#x | 1 0 2 | 0 2 0 0 0 1 0 | * * 2 * * * * * * | 0 1 1 0 0 ... o.x&#x | 1 0 2 | 0 2 0 0 0 0 1 | * * * 2 * * * * * | 0 1 0 1 0 ooo ooo&#x | 1 1 1 | 1 1 0 0 1 0 0 | * * * * 4 * * * * | 0 0 1 1 0 .x. .x. | 0 4 0 | 0 0 2 2 0 0 0 | * * * * * 1 * * * | 1 0 0 0 1 .xx ...&#x | 0 2 2 | 0 0 1 0 2 1 0 | * * * * * * 2 * * | 0 0 1 0 1 ... .xx&#x | 0 2 2 | 0 0 0 1 2 0 1 | * * * * * * * 2 * | 0 0 0 1 1 ..x ..x | 0 0 4 | 0 0 0 0 0 2 2 | * * * * * * * * 1 | 0 1 0 0 1 -----------+-------+---------------+-------------------+---------- ox. ox.&#x ♦ 1 4 0 | 4 0 2 2 0 0 0 | 2 2 0 0 0 1 0 0 0 | 1 * * * * o.x o.x&#x ♦ 1 0 4 | 0 4 0 0 0 2 2 | 0 0 2 2 0 0 0 0 1 | * 1 * * * oxx ...&#x ♦ 1 2 2 | 2 2 1 0 2 1 0 | 1 0 1 0 2 0 1 0 0 | * * 2 * * ... oxx&#x ♦ 1 2 2 | 2 2 0 1 2 0 1 | 0 1 0 1 2 0 0 1 0 | * * * 2 * .xx .xx&#x ♦ 0 4 4 | 0 0 2 2 4 2 2 | 0 0 0 0 0 1 2 2 1 | * * * * 1
or o.. o.. | 1 * ♦ 8 0 0 | 8 4 0 0 | 2 4 0 .o. .o. & | * 8 | 1 2 1 | 2 1 1 2 | 1 2 1 -------------+-----+-------+---------+------ oo. oo.&#x & | 1 1 | 8 * * | 2 1 0 0 | 1 2 0 .x. ... & | 0 2 | * 8 * | 1 0 1 1 | 1 1 1 .oo .oo&#x | 0 2 | * * 4 | 0 1 0 2 | 0 2 1 -------------+-----+-------+---------+------ ox. ...&#x & | 1 2 | 2 1 0 | 8 * * * | 1 1 0 ooo ooo&#x | 1 2 | 2 0 1 | * 4 * * | 0 2 0 .x. .x. & | 0 4 | 0 4 0 | * * 2 * | 1 0 1 .xx ...&#x & | 0 4 | 0 2 2 | * * * 4 | 0 1 1 -------------+-----+-------+---------+------ ox. ox.&#x & ♦ 1 4 | 4 4 0 | 4 0 1 0 | 2 * * oxx ...&#x & ♦ 1 4 | 4 2 2 | 2 2 0 1 | * 4 * .xx .xx&#x ♦ 0 8 | 0 8 4 | 0 0 2 4 | * * 1
{4} || squippy → height = 1/sqrt(2) = 0.707107
4 * * | 2 1 1 0 0 | 1 2 2 1 0 0 | 1 1 2 0
* 1 * ♦ 0 4 0 4 0 | 0 4 0 4 4 0 | 1 0 4 1
* * 4 | 0 0 1 1 2 | 0 0 2 1 2 1 | 0 1 2 1
--------+-----------+-------------+--------
2 0 0 | 4 * * * * | 1 1 1 0 0 0 | 1 1 1 0
1 1 0 | * 4 * * * | 0 2 0 1 0 0 | 1 0 2 0
1 0 1 | * * 4 * * | 0 0 2 1 0 0 | 0 1 2 0
0 1 1 | * * * 4 * | 0 0 0 1 2 0 | 0 0 2 1
0 0 2 | * * * * 4 | 0 0 1 0 1 1 | 0 1 1 1
--------+-----------+-------------+--------
4 0 0 | 4 0 0 0 0 | 1 * * * * * | 1 1 0 0
2 1 0 | 1 2 0 0 0 | * 4 * * * * | 1 0 1 0
2 0 2 | 1 0 2 0 1 | * * 4 * * * | 0 1 1 0
1 1 1 | 0 1 1 1 0 | * * * 4 * * | 0 0 2 0
0 1 2 | 0 0 0 2 1 | * * * * 4 * | 0 0 1 1
0 0 4 | 0 0 0 0 4 | * * * * * 1 | 0 1 0 1
--------+-----------+-------------+--------
♦ 4 1 0 | 4 4 0 0 0 | 1 4 0 0 0 0 | 1 * * *
♦ 4 0 4 | 4 0 4 0 4 | 1 0 4 0 0 1 | * 1 * *
♦ 2 1 2 | 1 2 2 2 1 | 0 1 1 2 1 0 | * * 4 *
♦ 0 1 4 | 0 0 0 4 4 | 0 0 0 0 4 1 | * * * 1
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