Acronym	esquidpy, J15
Name	elongated square dipyramid
	© ©
Vertex figure	[34], [32,42]
Lace city in approx. ASCII-art	o o o q q o o o
	x x w x x
Coordinates	(1/2, 1/2; 1/2)            & all changes of sign (0, 0; (1+sqrt(2))/2)   & all changes of sign
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	between {3} and {4}:   arccos[-sqrt(2/3)] = 144.735610° between {3} and {3}:   arccos(-1/3) = 109.471221° between {4} and {4}:   90°
Face vector	10, 20, 12
Confer	uniform relatives: cube   oct   related Johnson solids: squippy   esquipy   squobcu   general polytopal classes: Johnson solids   partial Stott expansions   bistratic lace towers
External links

Incidence matrix according to Dynkin symbol

oxxo4oooo&#xt   → height(1,2) = height(3,4) = 1/sqrt(2) = 0.707107
                 height(2,3) = 1
(pt || pseudo {4} || pseudo {4} || pt)

o...4o...    | 1 * * * | 4 0 0 0 0 | 4 0 0
.o..4.o..    | * 4 * * | 1 2 1 0 0 | 2 2 0
..o.4..o.    | * * 4 * | 0 0 1 2 1 | 0 2 2
...o4...o    | * * * 1 | 0 0 0 0 4 | 0 0 4
-------------+---------+-----------+------
oo..4oo..&#x | 1 1 0 0 | 4 * * * * | 2 0 0
.x.. ....    | 0 2 0 0 | * 4 * * * | 1 1 0
.oo.4.oo.&#x | 0 1 1 0 | * * 4 * * | 0 2 0
..x. ....    | 0 0 2 0 | * * * 4 * | 0 1 1
..oo4..oo&#x | 0 0 1 1 | * * * * 4 | 0 0 2
-------------+---------+-----------+------
ox.. ....&#x | 1 2 0 0 | 2 1 0 0 0 | 4 * *
.xx. ....&#x | 0 2 2 0 | 0 1 2 1 0 | * 4 *
..xo ....&#x | 0 0 2 1 | 0 0 0 1 2 | * * 4

or
o...4o...    & | 2 * | 4 0 0 | 4 0
.o..4.o..    & | * 8 | 1 2 1 | 2 2
---------------+-----+-------+----
oo..4oo..&#x & | 1 1 | 8 * * | 2 0
.x.. ....    & | 0 2 | * 8 * | 1 1
.oo.4.oo.&#x   | 0 2 | * * 4 | 0 2
---------------+-----+-------+----
ox.. ....&#x & | 1 2 | 2 1 0 | 8 *
.xx. ....&#x   | 0 4 | 0 2 2 | * 4

xox xwx&#xt   → both heights = 1/2
({4} || pseudo w-line || {4})

o.. o..    & | 8 * | 1 1 1 1 | 1 1 1 1
.o. .o.      | * 2 | 0 0 4 0 | 0 2 2 0
-------------+-----+---------+--------
x.. ...    & | 2 0 | 4 * * * | 1 1 0 0
... x..    & | 2 0 | * 4 * * | 1 0 0 1
oo. oo.&#x & | 1 1 | * * 8 * | 0 1 1 0
o.o o.o&#x   | 2 0 | * * * 4 | 0 0 1 1
-------------+-----+---------+--------
x.. x..    & | 4 0 | 2 2 0 0 | 2 * * *
xo. ...&#x & | 2 1 | 1 0 2 0 | * 4 * *
ooo ooo&#x   | 2 1 | 0 0 2 1 | * * 4 *
... x.x&#x   | 4 0 | 0 2 0 2 | * * * 2

x(xw)x o(qo)o&#xt   → both heights = 1/sqrt(2) = 0.707107
(line || pseudo diagonally elongated {4} || line)

o(..). o(..).    & | 4 * * | 1 2 1 0 0 | 2 2
.(o.). .(o.).      | * 4 * | 0 2 0 1 1 | 2 2
.(.o). .(.o).      | * * 2 | 0 0 2 0 2 | 0 4
-------------------+-------+-----------+----
x(..). .(..).    & | 2 0 0 | 2 * * * * | 2 0
o(o.). o(o.).&#x & | 1 1 0 | * 8 * * * | 1 1
o(.o). o(.o).&#x & | 1 0 1 | * * 4 * * | 0 2
.(x.). .(..).      | 0 2 0 | * * * 2 * | 2 0
.(oo). .(oo).&#x   | 0 1 1 | * * * * 4 | 0 2
-------------------+-------+-----------+----
x(x.). .(..).&#x & | 2 2 0 | 1 2 0 1 0 | 4 *
o(oo). o(oo).&#x & | 1 1 1 | 0 1 1 0 1 | * 8

wx ox4oo&#zx   → height = 0
(tegum sum of w-line and cube)

o. o.4o.    | 2 * | 4 0 0 | 0 4
.o .o4.o    | * 8 | 1 1 2 | 2 2
------------+-----+-------+----
oo oo4oo&#x | 1 1 | 8 * * | 0 2
.x .. ..    | 0 2 | * 4 * | 2 0
.. .x ..    | 0 2 | * * 8 | 1 1
------------+-----+-------+----
.x .x ..&#x | 0 4 | 0 2 2 | 4 *
.. ox ..&#x | 1 2 | 2 0 1 | * 8

qoo2oqo2xxw&#zx   → all heights = 0
(tegum sum of 2 orthogonal (q,x)-{4} and an intersection-parallel w-line)

o..2o..2o..    | 4 * * | 1 2 1 0 0 | 2 2
.o.2.o.2.o.    | * 4 * | 0 2 0 1 1 | 2 2
..o2..o2..o    | * * 2 | 0 0 2 0 2 | 0 4
---------------+-------+-----------+----
... ... x..    | 2 0 0 | 2 * * * * | 2 0
oo.2oo.2oo.&#x | 1 1 0 | * 8 * * * | 1 1
o.o2o.o2o.o&#x | 1 0 1 | * * 4 * * | 0 2
... ... .x.    | 0 2 0 | * * * 2 * | 2 0
.oo2.oo2.oo&#x | 0 1 1 | * * * * 4 | 0 2
---------------+-------+-----------+----
... ... xx.&#x | 2 2 0 | 1 2 0 1 0 | 4 *
ooo2ooo2ooo&#x | 1 1 1 | 0 1 1 0 1 | * 8