Acronym | squippyp, K-4.12 |
Name |
square-pyramidal prism, J1 prism, line || cube, digonal magnabicupolaic ring |
|,>,O device | line prism pyramid prism = ||>| |
Segmentochoron display | |
Circumradius | sqrt(3)/2 = 0.866025 |
Lace city in approx. ASCII-art |
x o x x x x |
Coordinates | (1/sqrt(2), 0, 0, 1/2) & all permutations in all but last coord., all changes of sign in all but first coord. |
Volume | sqrt(2)/6 = 0.235702 |
Dihedral angles | |
Face vector | 10, 21, 18, 7 |
Confer |
|
External links |
Incidence matrix according to Dynkin symbol
xx ox4oo&#x → height = 1/sqrt(2) = 0.707107
(line || cube)
o. o.4o. | 2 * | 1 4 0 0 | 4 4 0 0 | 4 1 0
.o .o4.o | * 8 | 0 1 1 2 | 1 2 2 1 | 2 1 1
------------+-----+---------+---------+------
x. .. .. | 2 0 | 1 * * * | 4 0 0 0 | 4 0 0
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
------------+-----+---------+---------+------
xx .. ..&#x | 2 2 | 1 2 1 0 | 4 * * * | 2 0 0
.. ox ..&#x | 1 2 | 0 2 0 1 | * 8 * * | 1 1 0
.x .x .. | 0 4 | 0 0 2 2 | * * 4 * | 1 0 1
.. .x4.o | 0 4 | 0 0 0 4 | * * * 2 | 0 1 1
------------+-----+---------+---------+------
xx ox ..&#x ♦ 2 4 | 1 4 2 2 | 2 2 1 0 | 4 * *
.. ox4oo&#x ♦ 1 4 | 0 4 0 4 | 0 4 0 1 | * 2 *
.x .x4.o ♦ 0 8 | 0 0 4 8 | 0 0 4 2 | * * 1
xx ox ox&#x → height = 1/sqrt(2) = 0.707107
(line || cube)
o. o. o. | 2 * | 1 4 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0
.o .o .o | * 8 | 0 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1
------------+-----+-----------+-------------+--------
x. .. .. | 2 0 | 1 * * * * | 4 0 0 0 0 0 | 2 2 0 0
oo oo oo&#x | 1 1 | * 8 * * * | 1 1 1 0 0 0 | 1 1 1 0
.x .. .. | 0 2 | * * 4 * * | 1 0 0 1 1 0 | 1 1 0 1
.. .x .. | 0 2 | * * * 4 * | 0 1 0 1 0 1 | 1 0 1 1
.. .. .x | 0 2 | * * * * 4 | 0 0 1 0 1 1 | 0 1 1 1
------------+-----+-----------+-------------+--------
xx .. ..&#x | 2 2 | 1 2 1 0 0 | 4 * * * * * | 1 1 0 0
.. ox ..&#x | 1 2 | 0 2 0 1 0 | * 4 * * * * | 1 0 1 0
.. .. ox&#x | 1 2 | 0 2 0 0 1 | * * 4 * * * | 0 1 1 0
.x .x .. | 0 4 | 0 0 2 2 0 | * * * 2 * * | 1 0 0 1
.x .. .x | 0 4 | 0 0 2 0 2 | * * * * 2 * | 0 1 0 1
.. .x .x | 0 4 | 0 0 0 2 2 | * * * * * 2 | 0 0 1 1
------------+-----+-----------+-------------+--------
xx ox ..&#x ♦ 2 4 | 1 4 2 2 0 | 2 2 0 1 0 0 | 2 * * *
xx .. ox&#x ♦ 2 4 | 1 4 2 0 2 | 2 0 2 0 1 0 | * 2 * *
.. ox ox&#x ♦ 1 4 | 0 4 0 2 2 | 0 2 2 0 0 1 | * * 2 *
.x .x .x ♦ 0 8 | 0 0 4 4 4 | 0 0 0 2 2 2 | * * * 1
oxx xxx&#x → height(1,2) = height(1,3) = sqrt(3)/2 = 0.866025 height(2,3) = 1 o.. o.. | 2 * * | 1 2 2 0 0 0 0 0 | 1 2 1 2 2 0 0 0 0 | 1 1 1 2 0 .o. .o. | * 4 * | 0 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 0 1 0 0 1 1 1 | 0 0 1 1 1 0 1 1 1 | 0 1 1 1 1 -----------+-------+-----------------+-------------------+---------- ... x.. | 2 0 0 | 1 * * * * * * * | 0 2 0 2 0 0 0 0 0 | 1 1 0 2 0 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 | 0 2 0 1 0 0 0 0 | 2 * * * * * * * * | 1 0 1 0 0 ... xx.&#x | 2 2 0 | 1 2 0 0 1 0 0 0 | * 2 * * * * * * * | 1 0 0 1 0 o.x ...&#x | 1 0 2 | 0 0 2 0 0 0 1 0 | * * 2 * * * * * * | 0 1 1 0 0 ... x.x&#x | 2 0 2 | 1 0 2 0 0 0 0 1 | * * * 2 * * * * * | 0 1 0 1 0 ooo ooo&#x | 1 1 1 | 0 1 1 0 0 1 0 0 | * * * * 4 * * * * | 0 0 1 1 0 .x. .x. | 0 4 0 | 0 0 0 2 2 0 0 0 | * * * * * 1 * * * | 1 0 0 0 1 .xx ...&#x | 0 2 2 | 0 0 0 1 0 2 1 0 | * * * * * * 2 * * | 0 0 1 0 1 ... .xx&#x | 0 2 2 | 0 0 0 0 1 2 0 1 | * * * * * * * 2 * | 0 0 0 1 1 ..x ..x | 0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * 1 | 0 1 0 0 1 -----------+-------+-----------------+-------------------+---------- ox. xx.&#x ♦ 2 4 0 | 1 4 0 2 2 0 0 0 | 2 2 0 0 0 1 0 0 0 | 1 * * * * o.x x.x&#x ♦ 2 0 4 | 1 0 4 0 0 0 2 2 | 0 0 2 2 0 0 0 0 1 | * 1 * * * oxx ...&#x ♦ 1 2 2 | 0 2 2 1 0 2 1 0 | 1 0 1 0 2 0 1 0 0 | * * 2 * * ... xxx&#x ♦ 2 2 2 | 1 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 0 2 2 4 2 2 | 0 0 0 0 0 1 2 2 1 | * * * * 1
{4} || trip → height = sqrt(2/3) = 0.816497
4 * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
* 2 * | 0 0 2 0 1 2 0 0 | 0 2 1 0 0 2 2 1 0 | 1 0 2 1 1
* * 4 | 0 0 0 1 0 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
--------+-----------------+-------------------+----------
2 0 0 | 2 * * * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
2 0 0 | * 2 * * * * * * | 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
1 1 0 | * * 4 * * * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
1 0 1 | * * * 4 * * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
0 2 0 | * * * * 1 * * * | 0 2 0 0 0 0 2 0 0 | 1 0 2 0 1
0 1 1 | * * * * * 4 * * | 0 0 0 0 0 1 1 1 0 | 0 0 1 1 1
0 0 2 | * * * * * * 2 * | 0 0 0 1 0 0 1 0 1 | 0 1 1 0 1
0 0 2 | * * * * * * * 2 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1
--------+-----------------+-------------------+----------
4 0 0 | 2 2 0 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
2 2 0 | 1 0 2 0 1 0 0 0 | * 2 * * * * * * * | 1 0 1 0 0
2 1 0 | 0 1 2 0 0 0 0 0 | * * 2 * * * * * * | 1 0 0 1 0
2 0 2 | 1 0 0 2 0 0 1 0 | * * * 2 * * * * * | 0 1 1 0 0
2 0 2 | 0 1 0 2 0 0 0 1 | * * * * 2 * * * * | 0 1 0 1 0
1 1 1 | 0 0 1 1 0 1 0 0 | * * * * * 4 * * * | 0 0 1 1 0
0 2 2 | 0 0 0 0 1 2 1 0 | * * * * * * 2 * * | 0 0 1 0 1
0 1 2 | 0 0 0 0 0 2 0 1 | * * * * * * * 2 * | 0 0 0 1 1
0 0 4 | 0 0 0 0 0 0 2 2 | * * * * * * * * 1 | 0 1 0 0 1
--------+-----------------+-------------------+----------
♦ 4 2 0 | 2 2 4 0 1 0 0 0 | 1 2 2 0 0 0 0 0 0 | 1 * * * *
♦ 4 0 4 | 2 2 0 4 0 0 2 2 | 1 0 0 2 2 0 0 0 1 | * 1 * * *
♦ 2 2 2 | 1 0 2 2 1 2 1 0 | 0 1 0 1 0 2 1 0 0 | * * 2 * *
♦ 2 1 2 | 0 1 2 2 0 2 0 1 | 0 0 1 0 1 2 0 1 0 | * * * 2 *
♦ 0 2 4 | 0 0 0 0 1 4 2 2 | 0 0 0 0 0 0 2 2 1 | * * * * 1
squippy || squippy → height = 1
1 * * * | 4 1 0 0 0 0 | 4 4 0 0 0 0 | 1 4 0 0 top-tip
* 4 * * | 1 0 2 1 0 0 | 2 1 1 0 0 0 | 1 2 1 0 top-base
* * 1 * | 0 1 0 0 4 0 | 0 4 0 0 4 0 | 0 4 0 1 bottom-tip
* * * 4 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1 bottom-base
----------+-------------+-------------+--------
1 1 0 0 | 4 * * * * * | 2 1 0 0 0 0 | 1 2 0 0
1 0 1 0 | * 1 * * * * | 0 4 0 0 0 0 | 0 4 0 0
0 2 0 0 | * * 4 * * * | 1 0 1 1 0 0 | 1 1 1 0
0 1 0 1 | * * * 4 * * | 0 1 0 2 0 0 | 0 2 1 0
0 0 1 1 | * * * * 4 * | 0 1 0 0 2 0 | 0 2 0 1
0 0 0 2 | * * * * * 4 | 0 0 0 1 1 1 | 0 1 1 1
----------+-------------+-------------+--------
1 2 0 0 | 2 0 1 0 0 0 | 4 * * * * * | 1 1 0 0
1 1 1 1 | 1 1 0 1 1 0 | * 4 * * * * | 0 2 0 0
0 4 0 0 | 0 0 4 0 0 0 | * * 1 * * * | 1 0 1 0
0 2 0 2 | 0 0 1 2 0 1 | * * * 4 * * | 0 1 1 0
0 0 1 2 | 0 0 0 0 2 1 | * * * * 4 * | 0 1 0 1
0 0 0 4 | 0 0 0 0 0 4 | * * * * * 1 | 0 0 1 1
----------+-------------+-------------+--------
♦ 1 4 0 0 | 4 0 4 0 0 0 | 4 0 1 0 0 0 | 1 * * *
♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 4 * *
♦ 0 4 0 4 | 0 0 4 4 0 4 | 0 0 1 4 0 1 | * * 1 *
♦ 0 0 1 4 | 0 0 0 0 4 4 | 0 0 0 0 4 1 | * * * 1
oxxo4oooo&#xr → height(1,2) = height(3,4) = sqrt(1-[1/4 *sin^2(π/n)]) height(1,4) = height(2,3) = 1 ( (pt || {4}) || (pt || {4}) ) o...4o... | 1 * * * | 4 1 0 0 0 0 | 4 4 0 0 0 0 | 1 4 0 0 .o..4.o.. | * 4 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0 ..o.4..o. | * * 4 * | 0 0 0 1 2 1 | 0 1 0 2 1 2 | 0 2 1 1 ...o4...o | * * * 1 | 0 1 0 0 0 4 | 0 4 0 0 0 4 | 0 4 0 1 --------------+---------+-------------+-------------+-------- oo..4oo..&#x | 1 1 0 0 | 4 * * * * * | 2 1 0 0 0 0 | 1 2 0 0 o..o4o..o&#x | 1 0 0 1 | * 1 * * * * | 0 4 0 0 0 0 | 0 4 0 0 .x.. .... | 0 2 0 0 | * * 4 * * * | 1 0 1 1 0 0 | 1 1 1 0 .oo.4.oo.&#x | 0 1 1 0 | * * * 4 * * | 0 1 0 2 0 0 | 0 2 1 0 ..x. .... | 0 0 2 0 | * * * * 4 * | 0 0 0 1 1 1 | 0 1 1 1 ..oo4..oo&#x | 0 0 1 1 | * * * * * 4 | 0 1 0 0 0 2 | 0 2 0 1 --------------+---------+-------------+-------------+-------- ox.. ....&#x | 1 2 0 0 | 2 0 1 0 0 0 | 4 * * * * * | 1 1 0 0 oooo4oooo&#xr | 1 1 1 1 | 1 1 0 1 0 1 | * 4 * * * * | 0 2 0 0 .x..4.o.. | 0 4 0 0 | 0 0 4 0 0 0 | * * 1 * * * | 1 0 1 0 .xx. ....&#x | 0 2 2 0 | 0 0 1 2 1 0 | * * * 4 * * | 0 1 1 0 ..x.4..o. | 0 0 4 0 | 0 0 0 0 4 0 | * * * * 1 * | 0 0 1 1 ..xo ....&#x | 0 0 2 1 | 0 0 0 0 1 2 | * * * * * 4 | 0 1 0 1 --------------+---------+-------------+-------------+-------- ox..4oo..&#x ♦ 1 4 0 0 | 4 0 4 0 0 0 | 4 0 1 0 0 0 | 1 * * * oxxo ....&#xr ♦ 1 2 2 1 | 2 1 1 2 1 2 | 1 2 0 1 0 1 | * 4 * * .xx.4.oo.&#x ♦ 0 4 4 0 | 0 0 4 4 4 0 | 0 0 1 4 1 0 | * * 1 * ..xo4..oo&#x ♦ 0 0 4 1 | 0 0 0 0 4 4 | 0 0 0 0 1 4 | * * * 1
o(xo)x4o(oo)o&#xt (pt || ({4} || pt) || para {4}) o(..).4o(..). | 1 * * * | 4 1 0 0 0 0 | 4 4 0 0 0 0 | 1 4 0 0 .(o.).4.(o.). | * 4 * * | 1 0 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0 .(.o).4.(.o). | * * 1 * | 0 1 0 0 4 0 | 0 4 0 0 4 0 | 0 4 0 1 .(..)o4.(..)o | * * * 4 | 0 0 0 1 1 2 | 0 1 0 2 2 1 | 0 2 1 1 ------------------+---------+-------------+-------------+-------- o(o.).4o(o.).&#x | 1 1 0 0 | 4 * * * * * | 2 1 0 0 0 0 | 1 2 0 0 o(.o).4o(.o).&#x | 1 0 1 0 | * 1 * * * * | 0 4 0 0 0 0 | 0 4 0 0 .(x.). .(..). | 0 2 0 0 | * * 4 * * * | 1 0 1 1 0 0 | 1 1 1 0 .(o.)o4.(o.)o&#x | 0 1 0 1 | * * * 4 * * | 0 1 0 2 0 0 | 0 2 1 0 .(.o)o4.(.o)o&#x | 0 0 1 1 | * * * * 4 * | 0 1 0 0 2 0 | 0 2 0 1 .(..)x .(..). | 0 0 0 2 | * * * * * 4 | 0 0 0 1 1 1 | 0 1 1 1 ------------------+---------+-------------+-------------+-------- o(x.). .(..).&#x | 1 2 0 0 | 2 0 1 0 0 0 | 4 * * * * * | 1 1 0 0 o(oo)o4o(oo)o&#xt | 1 1 1 1 | 1 1 0 1 1 0 | * 4 * * * * | 0 2 0 0 .(x.).4.(o.). | 0 4 0 0 | 0 0 4 0 0 0 | * * 1 * * * | 1 0 1 0 .(x.)x .(..).&#x | 0 2 0 2 | 0 0 1 2 0 1 | * * * 4 * * | 0 1 1 0 .(.o)x .(..).&#x | 0 0 1 2 | 0 0 0 0 2 1 | * * * * 4 * | 0 1 0 1 .(..)x4.(..)o | 0 0 0 4 | 0 0 0 0 0 4 | * * * * * 1 | 0 0 1 1 ------------------+---------+-------------+-------------+-------- o(x.).4o(o.).&#x ♦ 1 4 0 0 | 4 0 4 0 0 0 | 4 0 1 0 0 0 | 1 * * * o(xo)x .(..).&#xt ♦ 1 2 1 2 | 2 1 1 2 2 1 | 1 2 0 1 1 0 | * 4 * * .(x.)x4.(o.)o&#x ♦ 0 4 0 4 | 0 0 4 4 0 4 | 0 0 1 4 0 1 | * * 1 * .(.o)x4.(.o)o&#x ♦ 0 0 1 4 | 0 0 0 0 4 4 | 0 0 0 0 4 1 | * * * 1
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