Acronym op
TOCID symbol (8)P, t(4)P
Name octagonal prism,
bidiminished small rhombicuboctahedron
Circumradius sqrt[5+2 sqrt(2)]/2 = 1.398966
Vertex figure [42,8]
Coordinates ((1+sqrt(2))/2, 1/2, 1/2)   & all permutations in all but last coord., all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • between {4} and {4}:   135°
  • between {4} and {8}:   90°
Confer
general prisms:
n-p   n/d-p   2n-p  
variations:
q x8o   w x8o  
blends:
sroh   topfu  
general polytopal classes:
partial Stott expansions   segmentohedra  
External
links
wikipedia   WikiChoron   mathworld   quickfur

Incidence matrix according to Dynkin symbol

x x8o

. . . | 16 | 1  2 | 2 1
------+----+------+----
x . . |  2 | 8  * | 2 0
. x . |  2 | * 16 | 1 1
------+----+------+----
x x . |  4 | 2  2 | 8 *
. x8o |  8 | 0  8 | * 2

snubbed forms: x2s8o, s2s8o

x x4x

. . . | 16 | 1 1 1 | 1 1 1
------+----+-------+------
x . . |  2 | 8 * * | 1 1 0
. x . |  2 | * 8 * | 1 0 1
. . x |  2 | * * 8 | 0 1 1
------+----+-------+------
x x . |  4 | 2 2 0 | 4 * *
x . x |  4 | 2 0 2 | * 4 *
. x4x |  8 | 0 4 4 | * * 2	s2s4x

snubbed forms: x2s4x, x2β4x, s2s4x, β2β4x, x2s4s, s2s4s

xx8oo&#x   → height = 1
({8} || {8})

o.8o.    | 8 * | 2 1 0 | 1 2 0
.o8.o    | * 8 | 0 1 2 | 0 2 1
---------+-----+-------+------
x. ..    | 2 0 | 8 * * | 1 1 0
oo8oo&#x | 1 1 | * 8 * | 0 2 0
.x ..    | 0 2 | * * 8 | 0 1 1
---------+-----+-------+------
x.8o.    | 8 0 | 8 0 0 | 1 * *
xx ..&#x | 2 2 | 1 2 1 | * 8 *
.x8.o    | 0 8 | 0 0 8 | * * 1

xx4xx&#x   → height = 1
({8} || {8})

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

xxxx xwwx&#xt   → outer heights = 1/sqrt(2) = 0.707107
                  inner height = 1
({4} || pseudo (x,w)-{4} || pseudo (x,w)-{4} || {4})

o... o...     | 4 * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 0
.o.. .o..     | * 4 * * | 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 0
..o. ..o.     | * * 4 * | 0 0 0 0 1 1 1 0 0 | 0 0 1 1 1 0
...o ...o     | * * * 4 | 0 0 0 0 0 0 1 1 1 | 0 0 1 0 1 1
--------------+---------+-------------------+------------
x... ....     | 2 0 0 0 | 2 * * * * * * * * | 1 1 0 0 0 0
.... x...     | 2 0 0 0 | * 2 * * * * * * * | 1 0 1 0 0 0
oo.. oo..&#x  | 1 1 0 0 | * * 4 * * * * * * | 0 1 1 0 0 0
.x.. ....     | 0 2 0 0 | * * * 2 * * * * * | 0 1 0 1 0 0
.oo. .oo.&#x  | 0 1 1 0 | * * * * 4 * * * * | 0 0 1 1 0 0
..x. ....     | 0 0 2 0 | * * * * * 2 * * * | 0 0 0 1 1 0
..oo ..oo&#x  | 0 0 1 1 | * * * * * * 4 * * | 0 0 1 0 1 0
...x ....     | 0 0 0 2 | * * * * * * * 2 * | 0 0 0 0 1 1
.... ...x     | 0 0 0 2 | * * * * * * * * 2 | 0 0 1 0 0 1
--------------+---------+-------------------+------------
x... x...     | 4 0 0 0 | 2 2 0 0 0 0 0 0 0 | 1 * * * * *
xx.. ....&#x  | 2 2 0 0 | 1 0 2 1 0 0 0 0 0 | * 2 * * * *
.... xwwx&#xt | 2 2 2 2 | 0 1 2 0 2 0 2 0 1 | * * 2 * * *
.xx. ....&#x  | 0 2 2 0 | 0 0 0 1 2 1 0 0 0 | * * * 2 * *
..xx ....&#x  | 0 0 2 2 | 0 0 0 0 0 1 2 1 0 | * * * * 2 *
...x ...x     | 0 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * 1

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