Acronym	squacu, J4
Name	square cupola
VRML	⭳ ©
Circumradius	sqrt[5+2 sqrt(2)]/2 = 1.398966
Vertex figures	[3,43], [3,4,8]
Lace city in approx. ASCII-art	o q o x w w x
	x x x w w x
Volume	[3+2 sqrt(2)]/3 = 1.942809
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 {4} and {4}:   135° between {3} and {8}:   arccos[1/sqrt(3)] = 54.735610° between {4} and {8}:   45°
Face vector	12, 20, 10
Confer	general cupolae: n/d-cu   uniform relative: sirco   related Johnson solids: squobcu   esquigybcu   non-convex relative: rasquacu   general polytopal classes: Johnson solids   segmentohedra
External links

The square cupola is an edge-faceting of the small rhombicuboctahedron (sirco).

Incidence matrix according to Dynkin symbol

xx4ox&#x   → height = 1/sqrt(2) = 0.707107
({4} || {8})

o.4o.    | 4 * | 2 2 0 0 | 1 2 1 0
.o4.o    | * 8 | 0 1 1 1 | 0 1 1 1
---------+-----+---------+--------
x. ..    | 2 0 | 4 * * * | 1 1 0 0
oo4oo&#x | 1 1 | * 8 * * | 0 1 1 0
.x ..    | 0 2 | * * 4 * | 0 1 0 1
.. .x    | 0 2 | * * * 4 | 0 0 1 1
---------+-----+---------+--------
x.4o.    | 4 0 | 4 0 0 0 | 1 * * *
xx ..&#x | 2 2 | 1 2 1 0 | * 4 * *
.. ox&#x | 1 2 | 0 2 0 1 | * * 4 *
.x4.x    | 0 8 | 0 0 4 4 | * * * 1

so8ox&#x   → height = 1/sqrt(2) = 0.707107
({4} || {8})

demi( o.8o.    ) | 4 * | 2 2 0 0 | 1 1 0 2
      .o8.o      | * 8 | 0 1 1 1 | 0 1 1 1
-----------------+-----+---------+--------
sefa( s.8o.    ) | 2 0 | 4 * * * | 1 0 0 1
demi( oo8oo&#x ) | 1 1 | * 8 * * | 0 1 0 1
demi( .. .x    ) | 0 2 | * * 4 * | 0 0 1 1
demi( .. .x    ) | 0 2 | * * * 4 | 0 1 1 0
-----------------+-----+---------+--------
      s.8o.      | 4 0 | 4 0 0 0 | 1 * * *
demi( .. ox&#x ) | 1 2 | 0 2 0 1 | * 4 * *
      .o8.x      | 0 8 | 0 0 4 4 | * * 1 *
sefa( so8ox&#x ) | 2 2 | 1 2 1 0 | * * * 4

starting figure: xo8ox&#x

(oq)(xw) (qo)(wx)&#x   → height(1,2) = height(3,4) = 0
                         height(1,3) = height(2,4) = sqrt(3)/2 = 0.866025 

(o.)(..) (o.)(..)       | 2 * * * | 2 2 0 0 0 0 | 1 1 2 0 0
(.o)(..) (.o)(..)       | * 2 * * | 2 0 2 0 0 0 | 1 0 2 1 0
(..)(o.) (..)(o.)       | * * 4 * | 0 1 0 1 1 0 | 0 1 1 0 1
(..)(.o) (..)(.o)       | * * * 4 | 0 0 1 0 1 1 | 0 0 1 1 1
------------------------+---------+-------------+----------
(oo) ..  (oo) .. &#x    | 1 1 0 0 | 4 * * * * * | 1 0 1 0 0
(o.)(o.) (o.)(o.)&#x    | 1 0 1 0 | * 4 * * * * | 0 1 1 0 0
(.o)(.o) (.o)(.o)&#x    | 0 1 0 1 | * * 4 * * * | 0 0 1 1 0
 ..  x.   ..  ..        | 0 0 2 0 | * * * 2 * * | 0 1 0 0 1
 .. (oo)  .. (oo)&#x    | 0 0 1 1 | * * * * 4 * | 0 0 1 0 1
 ..  ..   ..  .x        | 0 0 0 2 | * * * * * 2 | 0 0 0 1 1
------------------------+---------+-------------+----------
(oq) ..  (qo) .. &#(zx) | 2 2 0 0 | 4 0 0 0 0 0 | 1 * * * *
(o.)(x.)  ..  .. &#x    | 1 0 2 0 | 0 2 0 1 0 0 | * 2 * * *
(oo)(oo) (oo)(oo)&#xr   | 1 1 1 1 | 1 1 1 0 1 0 | * * 4 * * cycle: (ABDC)
 ..  ..  (.o)(.x)&#x    | 0 1 0 2 | 0 0 2 0 0 1 | * * * 2 *
 .. (xw)  .. (wx)&#(zx) | 0 0 4 4 | 0 0 0 2 4 2 | * * * * 1