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 |
Volume | 2[1+sqrt(2)] = 4.828427 |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles |
|
Face vector | 16, 24, 10 |
Confer |
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External links |
The octagonal prism is an edge-faceting of the small rhombicuboctahedron (sirco).
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 snubbed forms: x2s4x, x2β4x, s2s4x (recta), 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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