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Acronym
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squasc (old: squippypy, alt: edihex), 4pyr-pyr, K-4.4
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Name
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square-scalene,
square-pyramidal pyramid,
line atop fully orthogonal square,
1/4-luna of hex,
4 tet rosette,
edge-diminished hex
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|,>,O device
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line prism pyramid pyramid = ||>>
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Circumradius
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1/sqrt(2) = 0.707107
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Lace city
in approx. ASCII-art
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o4o
o4o x4o
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x o
x o o x
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Coordinates
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-
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(0, 0, 0, 1/sqrt(2))
first tip
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(0, 0, 1/sqrt(2), 0)
second tip
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(1/sqrt(2), 0, 0, 0) & permutations and changes of sign in first 2 coordinates
square base
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(1/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))
tip
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(1/sqrt(8), 1/sqrt(8), -1/sqrt(8), -1/sqrt(8)) & all permutations except that with both minus in first 2 coordinates
squippy base
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General of army
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(is itself convex)
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Colonel of regiment
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(is itself locally convex)
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Dual
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(topologically selfdual, in different orientation)
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Dihedral angles
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Face vector
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6, 13, 13, 6
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Confer
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- uniform relative:
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hex
- related segmentochora:
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line || perp {n} (n=4)
n-af (n=2)
octpy
- general polytopal classes:
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luna
segmentochora
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External
links
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Incidence matrix according to Dynkin symbol
xo ox4oo&#x → height = 1/2
(pyramid product of line with {4})
o. o.4o. | 2 * ♦ 1 4 0 | 4 4 0 | 4 1
.o .o4.o | * 4 | 0 2 2 | 1 4 1 | 2 2
------------+-----+-------+-------+----
x. .. .. | 2 0 | 1 * * | 4 0 0 | 4 0
oo oo4oo&#x | 1 1 | * 8 * | 1 2 0 | 2 1
.. .x .. | 0 2 | * * 4 | 0 2 1 | 1 2
------------+-----+-------+-------+----
xo .. ..&#x | 2 1 | 1 2 0 | 4 * * | 2 0
.. ox ..&#x | 1 2 | 0 2 1 | * 8 * | 1 1
.. .x4.o | 0 4 | 0 0 4 | * * 1 | 0 2
------------+-----+-------+-------+----
xo ox ..&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 4 *
.. ox4oo&#x ♦ 1 4 | 0 4 4 | 0 4 1 | * 2
xo ox ox&#x → height = 1/2
(pyramid product of line with {4})
o. o.4o. | 2 * ♦ 1 4 0 0 | 4 2 2 0 | 2 2 1
.o .o4.o | * 4 | 0 2 1 1 | 1 2 2 1 | 1 1 2
------------+-----+---------+---------+------
x. .. .. | 2 0 | 1 * * * | 4 0 0 0 | 2 2 0
oo oo oo&#x | 1 1 | * 8 * * | 1 1 1 0 | 1 1 1
.. .x .. | 0 2 | * * 2 * | 0 2 0 1 | 1 0 2
.. .. .x | 0 2 | * * * 2 | 0 0 2 1 | 0 1 2
------------+-----+---------+---------+------
xo .. ..&#x | 2 1 | 1 2 0 0 | 4 * * * | 1 1 0
.. ox ..&#x | 1 2 | 0 2 1 0 | * 4 * * | 1 0 1
.. .. ox&#x | 1 2 | 0 2 0 1 | * * 4 * | 0 1 1
.. .x .x | 0 4 | 0 0 2 2 | * * * 1 | 0 0 2
------------+-----+---------+---------+------
xo ox ..&#x ♦ 2 2 | 1 4 1 0 | 2 2 0 0 | 2 * *
xo .. ox&#x ♦ 2 2 | 1 4 0 1 | 2 0 2 0 | * 2 *
.. ox ox&#x ♦ 1 4 | 0 4 2 2 | 0 2 2 1 | * * 2
oox4ooo&#x → height(1,2) = 1
height(1,3) = height(2,3) = 1/sqrt(2) = 0.707107
o.. o.. | 1 * * ♦ 1 4 0 0 | 4 4 0 0 | 4 1 0
.o. .o. | * 1 * ♦ 1 0 4 0 | 4 0 4 0 | 4 0 1
..o ..o | * * 4 | 0 1 1 2 | 1 2 2 1 | 2 1 1
-----------+-------+---------+---------+------
oo.4oo.&#x | 1 1 0 | 1 * * * | 4 0 0 0 | 4 0 0
o.o4o.o&#x | 1 0 1 | * 4 * * | 1 2 0 0 | 2 1 0
.oo4.oo&#x | 0 1 1 | * * 4 * | 1 0 2 0 | 2 0 1
..x ... | 0 0 2 | * * * 4 | 0 1 1 1 | 1 1 1
-----------+-------+---------+---------+------
ooo4ooo&#x | 1 1 1 | 1 1 1 0 | 4 * * * | 2 0 0
o.x ...&#x | 1 0 2 | 0 2 0 1 | * 4 * * | 1 1 0
.ox ...&#x | 0 1 2 | 0 0 2 1 | * * 4 * | 1 0 1
..x4..o | 0 0 4 | 0 0 0 4 | * * * 1 | 0 1 1
-----------+-------+---------+---------+------
oox ...&#x ♦ 1 1 2 | 1 2 2 1 | 2 1 1 0 | 4 * *
o.x4o.o&#x ♦ 1 0 4 | 0 4 0 4 | 0 4 0 1 | * 1 *
.ox4.oo&#x ♦ 0 1 4 | 0 0 4 4 | 0 0 4 1 | * * 1
or
o.. o.. & | 2 * ♦ 1 4 0 | 4 4 0 | 4 1
..o ..o | * 4 | 0 2 2 | 1 4 1 | 2 2
-------------+-----+-------+-------+----
oo.4oo.&#x | 2 0 | 1 * * | 4 0 0 | 4 0
o.o4o.o&#x & | 1 1 | * 8 * | 1 2 0 | 2 1
..x ... | 0 2 | * * 4 | 0 2 1 | 1 2
-------------+-----+-------+-------+----
ooo4ooo&#x | 2 1 | 1 2 0 | 4 * * | 2 0
o.x ...&#x & | 1 2 | 0 2 1 | * 8 * | 1 1
..x4..o | 0 4 | 0 0 4 | * * 1 | 0 2
-------------+-----+-------+-------+----
oox ...&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 4 *
o.x4o.o&#x & ♦ 1 4 | 0 4 4 | 0 4 1 | * 2
oox oox&#x → height(1,2) = 1
height(1,3) = height(2,3) = 1/sqrt(2) = 0.707107
o.. o.. | 1 * * ♦ 1 4 0 0 0 | 4 2 2 0 0 0 | 2 2 1 0
.o. .o. | * 1 * ♦ 1 0 4 0 0 | 4 0 0 2 2 0 | 2 2 0 1
..o ..o | * * 4 | 0 1 1 1 1 | 1 1 1 1 1 1 | 1 1 1 1
-----------+-------+-----------+-------------+--------
oo. oo.&#x | 1 1 0 | 1 * * * * | 4 0 0 0 0 0 | 2 2 0 0
o.o o.o&#x | 1 0 1 | * 4 * * * | 1 1 1 0 0 0 | 1 1 1 0
.oo .oo&#x | 0 1 1 | * * 4 * * | 1 0 0 1 1 0 | 1 1 0 1
..x ... | 0 0 2 | * * * 2 * | 0 1 0 1 0 1 | 1 0 1 1
... ..x | 0 0 2 | * * * * 2 | 0 0 1 0 1 1 | 0 1 1 1
-----------+-------+-----------+-------------+--------
ooo ooo&#x | 1 1 1 | 1 1 1 0 0 | 4 * * * * * | 1 1 0 0
o.x ...&#x | 1 0 2 | 0 2 0 1 0 | * 2 * * * * | 1 0 1 0
... o.x&#x | 1 0 2 | 0 2 0 0 1 | * * 2 * * * | 0 1 1 0
.ox ...&#x | 0 1 2 | 0 0 2 1 0 | * * * 2 * * | 1 0 0 1
... .ox&#x | 0 1 2 | 0 0 2 0 1 | * * * * 2 * | 0 1 0 1
..x ..x | 0 0 4 | 0 0 0 2 2 | * * * * * 1 | 0 0 1 1
-----------+-------+-----------+-------------+--------
oox ...&#x ♦ 1 1 2 | 1 2 2 1 0 | 2 1 0 1 0 0 | 2 * * *
... oox&#x ♦ 1 1 2 | 1 2 2 0 1 | 2 0 1 0 1 0 | * 2 * *
o.x o.x&#x ♦ 1 0 4 | 0 4 0 4 0 | 0 2 2 0 0 1 | * * 1 *
.ox .ox&#x ♦ 0 1 4 | 0 0 4 4 0 | 0 0 0 2 2 1 | * * * 1
or
o.. o.. & | 2 * ♦ 1 4 0 | 4 4 0 | 4 1
..o ..o | * 4 | 0 2 2 | 1 4 1 | 2 2
-------------+-----+-------+-------+----
oo. oo.&#x | 2 0 | 1 * * | 4 0 0 | 4 0
o.o o.o&#x & | 1 1 | * 8 * | 1 2 0 | 2 1
..x ... & | 0 2 | * * 4 | 0 2 1 | 1 2
-------------+-----+-------+-------+----
ooo ooo&#x | 2 1 | 1 2 0 | 4 * * | 2 0
o.x ...&#x & | 1 2 | 0 2 1 | * 8 * | 1 1
..x ..x | 0 4 | 0 0 4 | * * 1 | 0 2
-------------+-----+-------+-------+----
oox ...&#x & ♦ 2 2 | 1 4 1 | 2 2 0 | 4 *
o.x o.x&#x & ♦ 1 4 | 0 4 4 | 0 4 1 | * 2
pt || squippy → height = 1/sqrt(2) = 0.707107
o.. o.. | 1 * * ♦ 1 4 0 0 | 4 4 0 0 | 4 1 0
.o. .o. | * 1 * ♦ 1 0 4 0 | 4 0 4 0 | 4 0 1
..o ..o | * * 4 | 0 1 1 2 | 1 2 2 1 | 2 1 1
-----------+-------+---------+---------+------
oo.4oo.&#x | 1 1 0 | 1 * * * | 4 0 0 0 | 4 0 0
o.o4o.o&#x | 1 0 1 | * 4 * * | 1 2 0 0 | 2 1 0
.oo4.oo&#x | 0 1 1 | * * 4 * | 1 0 2 0 | 2 0 1
..x ... | 0 0 2 | * * * 4 | 0 1 1 1 | 1 1 1
-----------+-------+---------+---------+------
ooo4ooo&#x | 1 1 1 | 1 1 1 0 | 4 * * * | 2 0 0
o.x ...&#x | 1 0 2 | 0 2 0 1 | * 4 * * | 1 1 0
.ox ...&#x | 0 1 2 | 0 0 2 1 | * * 4 * | 1 0 1
..x4..o | 0 0 4 | 0 0 0 4 | * * * 1 | 0 1 1
-----------+-------+---------+---------+------
oox ...&#x ♦ 1 1 2 | 1 2 2 1 | 2 1 1 0 | 4 * *
o.x4o.o&#x ♦ 1 0 4 | 0 4 0 4 | 0 4 0 1 | * 1 *
.ox4.oo&#x ♦ 0 1 4 | 0 0 4 4 | 0 0 4 1 | * * 1
xoo oxx&#x → height(1,2) = height(1,3) = 1/sqrt(2) = 0.707107
height(2,3) = 1
o.. o.. | 2 * * ♦ 1 2 2 0 0 0 | 2 1 2 1 2 0 | 1 1 2 1
.o. .o. | * 2 * | 0 2 0 1 1 0 | 1 2 0 0 2 1 | 1 0 1 2
..o ..o | * * 2 | 0 0 2 0 1 1 | 0 0 1 2 2 1 | 0 1 1 2
-----------+-------+-------------+-------------+--------
x.. ... | 2 0 0 | 1 * * * * * | 2 0 2 0 0 0 | 1 1 2 0
oo. oo.&#x | 1 1 0 | * 4 * * * * | 1 1 0 0 1 0 | 1 0 1 1
o.o o.o&#x | 1 0 1 | * * 4 * * * | 0 0 1 1 1 0 | 0 1 1 1
... .x. | 0 2 0 | * * * 1 * * | 0 2 0 0 0 1 | 1 0 0 2
.oo .oo&#x | 0 1 1 | * * * * 2 * | 0 0 0 0 2 1 | 0 0 1 2
... ..x | 0 0 2 | * * * * * 1 | 0 0 0 2 0 1 | 0 1 0 2
-----------+-------+-------------+-------------+--------
xo. ...&#x | 2 1 0 | 1 2 0 0 0 0 | 2 * * * * * | 1 0 1 0
... ox.&#x | 1 2 0 | 0 2 0 1 0 0 | * 2 * * * * | 1 0 0 1
x.o ...&#x | 2 0 1 | 1 0 2 0 0 0 | * * 2 * * * | 0 1 1 0
... o.x&#x | 1 0 2 | 0 0 2 0 0 1 | * * * 2 * * | 0 1 0 1
ooo ooo&#x | 1 1 1 | 0 1 1 0 1 0 | * * * * 4 * | 0 0 1 1
... .xx&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * 1 | 0 0 0 2
-----------+-------+-------------+-------------+--------
xo. ox.&#x ♦ 2 2 0 | 1 4 0 1 0 0 | 2 2 0 0 0 0 | 1 * * *
x.o o.x&#x ♦ 2 0 2 | 1 0 4 0 0 1 | 0 0 2 2 0 0 | * 1 * *
xoo ...&#x ♦ 2 1 1 | 1 2 2 0 1 0 | 1 0 1 0 2 0 | * * 2 *
... oxx&#x ♦ 1 2 2 | 0 2 2 1 2 1 | 0 1 0 1 2 1 | * * * 2
or
o.. o.. | 2 * ♦ 1 4 0 0 | 4 2 2 0 | 2 2 1
.o. .o. & | * 4 | 0 2 1 1 | 1 2 2 1 | 1 1 2
-------------+-----+---------+---------+------
x.. ... | 2 0 | 1 * * * | 4 0 0 0 | 2 2 0
oo. oo.&#x & | 1 1 | * 8 * * | 1 1 1 0 | 1 1 1
... .x. & | 0 2 | * * 2 * | 0 2 0 1 | 1 0 2
.oo .oo&#x | 0 2 | * * * 2 | 0 0 2 1 | 0 1 2
-------------+-----+---------+---------+------
xo. ...&#x & | 2 1 | 1 2 0 0 | 4 * * * | 1 1 0
... ox.&#x & | 1 2 | 0 2 1 0 | * 4 * * | 1 0 1
ooo ooo&#x | 1 2 | 0 2 0 1 | * * 4 * | 0 1 1
... .xx&#x | 0 4 | 0 0 2 2 | * * * 1 | 0 0 2
-------------+-----+---------+---------+------
xo. ox.&#x & ♦ 2 2 | 1 4 1 0 | 2 2 0 0 | 2 * *
xoo ...&#x ♦ 2 2 | 1 4 0 1 | 2 0 2 0 | * 2 *
... oxx&#x ♦ 1 4 | 0 4 2 2 | 0 2 2 1 | * * 2
xoox&#x → height(1,2) = height(1,3) = height(2,4) = height(3,4) = sqrt(3)/2 = 0.866025
height(1,4) = height(2,3) = 1
o... | 2 * * * | 1 1 1 1 0 0 0 0 | 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
.o.. | * 1 * * ♦ 0 2 0 0 1 2 0 0 | 1 0 0 2 2 0 2 1 0 | 1 1 0 2 1
..o. | * * 1 * ♦ 0 0 2 0 1 0 2 0 | 0 1 0 2 0 2 2 0 1 | 1 0 1 2 1
...o | * * * 2 | 0 0 0 1 0 1 1 1 | 0 0 1 0 1 1 1 1 1 | 0 1 1 1 1
--------+---------+-----------------+-------------------+----------
x... | 2 0 0 0 | 1 * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0
oo..&#x | 1 1 0 0 | * 2 * * * * * * | 1 0 0 1 1 0 0 0 0 | 1 1 0 1 0
o.o.&#x | 1 0 1 0 | * * 2 * * * * * | 0 1 0 1 0 1 0 0 0 | 1 0 1 1 0
o..o&#x | 1 0 0 1 | * * * 2 * * * * | 0 0 1 0 1 1 0 0 0 | 0 1 1 1 0
.oo.&#x | 0 1 1 0 | * * * * 1 * * * | 0 0 0 2 0 0 2 0 0 | 1 0 0 2 1
.o.o&#x | 0 1 0 1 | * * * * * 2 * * | 0 0 0 0 1 0 1 1 0 | 0 1 0 1 1
..oo&#x | 0 0 1 1 | * * * * * * 2 * | 0 0 0 0 0 1 1 0 1 | 0 0 1 1 1
...x | 0 0 0 2 | * * * * * * * 1 | 0 0 1 0 0 0 0 1 1 | 0 1 1 0 1
--------+---------+-----------------+-------------------+----------
xo..&#x | 2 1 0 0 | 1 2 0 0 0 0 0 0 | 1 * * * * * * * * | 1 1 0 0 0
x.o.&#x | 2 0 1 0 | 1 0 2 0 0 0 0 0 | * 1 * * * * * * * | 1 0 1 0 0
x..x&#x | 2 0 0 2 | 1 0 0 2 0 0 0 1 | * * 1 * * * * * * | 0 1 1 0 0
ooo.&#x | 1 1 1 0 | 0 1 1 0 1 0 0 0 | * * * 2 * * * * * | 1 0 0 1 0
oo.o&#x | 1 1 0 1 | 0 1 0 1 0 1 0 0 | * * * * 2 * * * * | 0 1 0 1 0
o.oo&#x | 1 0 1 1 | 0 0 1 1 0 0 1 0 | * * * * * 2 * * * | 0 0 1 1 0
.ooo&#x | 0 1 1 1 | 0 0 0 0 1 1 1 0 | * * * * * * 2 * * | 0 0 0 1 1
.o.x&#x | 0 1 0 2 | 0 0 0 0 0 2 0 1 | * * * * * * * 1 * | 0 1 0 0 1
..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 2 1 | * * * * * * * * 1 | 0 0 1 0 1
--------+---------+-----------------+-------------------+----------
xoo.&#x ♦ 2 1 1 0 | 1 2 2 0 1 0 0 0 | 1 1 0 2 0 0 0 0 0 | 1 * * * *
xo.x&#x ♦ 2 1 0 2 | 1 2 0 2 0 2 0 1 | 1 0 1 0 2 0 0 1 0 | * 1 * * *
x.ox&#x ♦ 2 0 1 2 | 1 0 2 2 0 0 2 1 | 0 1 1 0 0 2 0 0 1 | * * 1 * *
oooo&#x ♦ 1 1 1 1 | 0 1 1 1 1 1 1 0 | 0 0 0 1 1 1 1 0 0 | * * * 2 *
.oox&#x ♦ 0 1 1 2 | 0 0 0 0 1 2 2 1 | 0 0 0 0 0 0 2 1 1 | * * * * 1