| Acronym | (n/d,m/b)-gybef |
| Name |
(n/d,m/b)-gyrobifastegium, {n/d} atop (n/d,m/b)-duoprism atop perpendicular {m/b} |
| Circumradius | ... |
| Face vector | n+m+nm, n+m+4nm, 2+n+m+5nm, 3n+3m+2nm, 2n+2m |
| Especially | 3-gybef (n/d=m/b=3) 4-gybef (n/d=m/b=4) |
Just as the 3D gyrobifastegium just was the bistratic lace tower, obtained as external blend of 2 square-adjoined trips (then in the sense of line || pseudo square || perp line), this 5D (n/d,m/b)-gyrobifastegium likewise is the bistratic adjoin of an ({n/d}, {m/b}-pyr)-duoprism with an ({n/d}-pyr, {m/b})-duoprism, thereby blending out the common ({n/d}, {m/b})-duoprismatic base.
The below given heights formulae directly show the additional restrictions on n/d, m/b, directly obtained from the according height restriction of the according polygrammic pyramids:
n/d, m/b ∈ ]6/5,2[ ∪ ]2,6[
Incidence matrix according to Dynkin symbol
xxo-n/d-ooo oxx-m/b-ooo&#xt → height(1,2) = sqrt(1-1/[4 sin2(π b/m)])
heigh(2,3) = sqrt(1-1/[4 sin2(π d/n)])
({n/d} || pseudo (n/d,m/b)-duoprism || perp {m/b})
o..-n/d-o.. o..-m/b-o.. | n * * | 2 m 0 0 0 0 | 1 2m m 0 0 0 0 0 0 | m 2m 1 0 0 0 0 0 | m 2 0 0
.o.-n/d-.o. .o.-m/b-.o. | * nm * | 0 1 2 2 1 0 | 0 2 2 1 4 1 2 2 0 | 1 4 1 2 2 1 4 1 | 2 2 2 2
..o-n/d-..o ..o-m/b-..o | * * m | 0 0 0 0 n 2 | 0 0 0 0 0 0 n 2n 1 | 0 0 0 0 0 1 2n n | 0 0 2 n
---------------------------+--------+-----------------+------------------------+-------------------+--------
x.. ... ... ... | 2 0 0 | n * * * * * | 1 m 0 0 0 0 0 0 0 | m m 0 0 0 0 0 0 | m 1 0 0
oo.-n/d-oo. oo.-m/b-oo.&#x | 1 1 0 | * nm * * * * | 0 2 2 0 0 0 0 0 0 | 1 4 1 0 0 0 0 0 | 2 2 0 0
.x. ... ... ... | 0 2 0 | * * nm * * * | 0 1 0 1 2 0 1 0 0 | 1 2 0 2 1 1 2 0 | 2 1 2 1
... ... .x. ... | 0 2 0 | * * * nm * * | 0 0 1 0 2 1 0 1 0 | 0 2 1 1 2 0 2 1 | 1 2 1 2
.oo-n/d-.oo .oo-m/b-.oo&#x | 0 1 1 | * * * * nm * | 0 0 0 0 0 0 2 2 0 | 0 0 0 0 0 1 4 1 | 0 0 2 2
... ... ..x ... | 0 0 2 | * * * * * m | 0 0 0 0 0 0 0 n 1 | 0 0 0 0 0 0 n n | 0 0 1 n
---------------------------+--------+-----------------+------------------------+-------------------+--------
x..-n/d-o.. ... ... | n 0 0 | n 0 0 0 0 0 | 1 * * * * * * * * | m 0 0 0 0 0 0 0 | m 0 0 0
xx. ... ... ...&#x | 2 2 0 | 1 2 1 0 0 0 | * nm * * * * * * * | 2 1 0 0 0 0 0 0 | 2 1 0 0
... ... ox. ...&#x | 1 2 0 | 0 2 0 1 0 0 | * * nm * * * * * * | 0 2 1 0 0 0 0 0 | 1 2 0 0
.x.-n/d-.o. ... ... | 0 n 0 | 0 0 n 0 0 0 | * * * m * * * * * | 1 0 0 2 0 1 0 0 | 2 0 2 0
.x. ... .x. ... | 0 4 0 | 0 0 2 2 0 0 | * * * * nm * * * * | 0 1 0 1 1 0 1 0 | 1 1 1 1
... ... .x.-m/b-.o. | 0 m 0 | 0 0 0 m 0 0 | * * * * * n * * * | 0 0 1 0 2 0 0 1 | 0 2 0 2
.xo ... ... ...&#x | 0 2 1 | 0 0 1 0 2 0 | * * * * * * nm * * | 0 0 0 0 0 1 2 0 | 0 0 2 1
... ... .xx ...&#x | 0 2 2 | 0 0 0 1 2 1 | * * * * * * * nm * | 0 0 0 0 0 0 2 1 | 0 0 1 2
... ... ..x-m/b-..o | 0 0 m | 0 0 0 0 0 m | * * * * * * * * 1 | 0 0 0 0 0 0 0 n | 0 0 0 n
---------------------------+--------+-----------------+------------------------+-------------------+--------
xx.-n/d-oo. ... ...&#x ♦ n n 0 | n n n 0 0 0 | 1 n 0 1 0 0 0 0 0 | m * * * * * * * | 2 0 0 0
xx. ... ox. ...&#x ♦ 2 4 0 | 1 4 2 2 0 0 | 0 2 2 0 1 0 0 0 0 | * nm * * * * * * | 1 1 0 0
... ... ox.-m/b-oo.&#x ♦ 1 m 0 | 0 m 0 m 0 0 | 0 0 m 0 0 1 0 0 0 | * * n * * * * * | 0 2 0 0
.x.-n/d-.o. .x. ... ♦ 0 2n 0 | 0 0 2n n 0 0 | 0 0 0 2 n 0 0 0 0 | * * * m * * * * | 1 0 1 0
.x. ... .x.-m/b-.o. ♦ 0 2m 0 | 0 0 m 2m 0 0 | 0 0 0 0 m 2 0 0 0 | * * * * n * * * | 0 1 0 1
.xo-n/d-.oo ... ...&#x ♦ 0 n 1 | 0 0 n 0 n 0 | 0 0 0 1 0 0 n 0 0 | * * * * * m * * | 0 0 2 0
.xo ... .xx ...&#x ♦ 0 4 2 | 0 0 2 2 4 1 | 0 0 0 0 1 0 2 2 0 | * * * * * * nm * | 0 0 1 1
... ... .xx-m/b-.oo&#x ♦ 0 m m | 0 0 0 m m m | 0 0 0 0 0 1 0 m 1 | * * * * * * * n | 0 0 0 2
---------------------------+--------+-----------------+------------------------+-------------------+--------
xx.-n/d-oo. ox. ...&#x ♦ n 2n 0 | n 2n 2n n 0 0 | 1 2n n 2 n 0 0 0 0 | 2 n 0 1 0 0 0 0 | m * * *
xx. ... ox.-m/b-oo.&#x ♦ 2 2m 0 | 1 2m m 2m 0 0 | 0 m 2m 0 m 2 0 0 0 | 0 m 2 0 1 0 0 0 | * n * *
.xo-n/d-.oo .xx ...&#x ♦ 0 2n 2 | 0 0 2n n 2n 1 | 0 0 0 2 n 0 2n n 0 | 0 0 0 1 0 2 n 0 | * * m *
.xo ... .xx-m/b-.oo&#x ♦ 0 2m 4 | 0 0 m 2m 2m m | 0 0 0 0 m 2 m 2m 1 | 0 0 0 0 1 0 m 2 | * * * n
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