Acronym	podip
Name	pentagon - octagon duoprism
Circumradius	sqrt[(15+5 sqrt(2)+sqrt(5))/10] = 1.559075
Volume	[1+sqrt(2)] sqrt[25+10 sqrt(5)]/2 = 8.307200
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex)
Dihedral angles	at {5} between pip and pip:   135° at {8} between op and op:   108° at {4} between pip and op:   90°
Face vector	40, 80, 53, 13
Confer	general duoprisms: n,m-dip   2n,m-dip   5,n-dip   8,n-dip   general polytopal classes: bistratic lace towers
External links

Incidence matrix according to Dynkin symbol

x5o x8o

. . . . | 40 |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 40  * | 1  2 0 | 2 1
. . x . |  2 |  * 40 | 0  2 1 | 1 2
--------+----+-------+--------+----
x5o . . |  5 |  5  0 | 8  * * | 2 0
x . x . |  4 |  2  2 | * 40 * | 1 1
. . x8o |  8 |  0  8 | *  * 5 | 0 2
--------+----+-------+--------+----
x5o x . ♦ 10 | 10  5 | 2  5 0 | 8 *
x . x8o ♦ 16 |  8 16 | 0  8 2 | * 5

x4x x5o

. . . . | 40 |  1  1  2 | 1  2  2 1 | 2 1 1
--------+----+----------+-----------+------
x . . . |  2 | 20  *  * | 1  2  0 0 | 2 1 0
. x . . |  2 |  * 20  * | 1  0  2 0 | 2 0 1
. . x . |  2 |  *  * 40 | 0  1  1 1 | 1 1 1
--------+----+----------+-----------+------
x4x . . |  8 |  4  4  0 | 5  *  * * | 2 0 0
x . x . |  4 |  2  0  2 | * 20  * * | 1 1 0
. x x . |  4 |  0  2  2 | *  * 20 * | 1 0 1
. . x5o |  5 |  0  0  5 | *  *  * 8 | 0 1 1
--------+----+----------+-----------+------
x4x x . ♦ 16 |  8  8  8 | 2  4  4 0 | 5 * *
x . x5o ♦ 10 |  5  0 10 | 0  5  0 2 | * 4 *
. x x5o ♦ 10 |  0  5 10 | 0  0  5 2 | * * 4

ofx xxx8ooo&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
                    height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({8} || pseudo (f,x)-op || op)

o.. o..8o..     | 8  *  * | 2  2  0  0 0  0 | 1 1  4 0  0 0 0 | 2 2 0 0
.o. .o.8.o.     | * 16  * | 0  1  2  1 0  0 | 0 1  2 1  2 0 0 | 2 1 1 0
..o ..o8..o     | *  * 16 | 0  0  0  1 1  2 | 0 1  0 0  2 2 1 | 2 0 1 1
----------------+---------+-----------------+-----------------+--------
... x.. ...     | 2  0  0 | 8  *  *  * *  * | 1 0  2 0  0 0 0 | 1 2 0 0
oo. oo.8oo.&#x  | 1  1  0 | * 16  *  * *  * | 0 1  2 0  0 0 0 | 2 1 0 0
... .x. ...     | 0  2  0 | *  * 16  * *  * | 0 0  1 1  1 0 0 | 1 1 1 0
.oo .oo8.oo&#x  | 0  1  1 | *  *  * 16 *  * | 0 1  0 0  2 0 0 | 2 0 1 0
..x ... ...     | 0  0  2 | *  *  *  * 8  * | 0 1  0 0  0 2 0 | 2 0 0 1
... ..x ...     | 0  0  2 | *  *  *  * * 16 | 0 0  0 0  1 1 1 | 1 0 1 1
----------------+---------+-----------------+-----------------+--------
... x..8o..     | 8  0  0 | 8  0  0  0 0  0 | 1 *  * *  * * * | 0 2 0 0
ofx ... ...&#xt | 1  2  2 | 0  2  0  2 1  0 | * 8  * *  * * * | 2 0 0 0
... xx. ...&#x  | 2  2  0 | 1  2  1  0 0  0 | * * 16 *  * * * | 1 1 0 0
... .x.8.o.     | 0  8  0 | 0  0  8  0 0  0 | * *  * 2  * * * | 0 1 1 0
... .xx ...&#x  | 0  2  2 | 0  0  1  2 0  1 | * *  * * 16 * * | 1 0 1 0
..x ..x ...     | 0  0  4 | 0  0  0  0 2  2 | * *  * *  * 8 * | 1 0 0 1
... ..x8..o     | 0  0  8 | 0  0  0  0 0  8 | * *  * *  * * 2 | 0 0 1 1
----------------+---------+-----------------+-----------------+--------
ofx xxx ...&#xt ♦ 2  4  4 | 1  4  2  4 2  2 | 0 2  2 0  2 1 0 | 8 * * *
... xx.8oo.&#x  ♦ 8  8  0 | 8  8  8  0 0  0 | 1 0  8 1  0 0 0 | * 2 * *
... .xx8.oo&#x  ♦ 0  8  8 | 0  0  8  8 0  8 | 0 0  0 1  8 0 1 | * * 2 *
..x ..x8..o     ♦ 0  0 16 | 0  0  0  0 8 16 | 0 0  0 0  0 8 2 | * * * 1

ofx xxx4xxx&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
                    height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({8} || pseudo (f,x)-op || op)

o.. o..4o..     | 8  *  * | 1 1  2 0 0  0 0 0 0 | 1 1 2 2 0 0 0 0 0 0 | 1 1 2 0 0
.o. .o.4.o.     | * 16  * | 0 0  1 1 1  1 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
..o ..o4..o     | *  * 16 | 0 0  0 0 0  1 1 1 1 | 0 1 0 0 0 1 1 1 1 1 | 1 1 0 1 1
----------------+---------+---------------------+---------------------+----------
... x.. ...     | 2  0  0 | 4 *  * * *  * * * * | 1 0 2 0 0 0 0 0 0 0 | 1 0 2 0 0
... ... x..     | 2  0  0 | * 4  * * *  * * * * | 1 0 0 2 0 0 0 0 0 0 | 0 1 2 0 0
oo. oo.4oo.&#x  | 1  1  0 | * * 16 * *  * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0
... .x. ...     | 0  2  0 | * *  * 8 *  * * * * | 0 0 1 0 1 1 0 0 0 0 | 1 0 1 1 0
... ... .x.     | 0  2  0 | * *  * * 8  * * * * | 0 0 0 1 1 0 1 0 0 0 | 0 1 1 1 0
.oo .oo4.oo&#x  | 0  1  1 | * *  * * * 16 * * * | 0 1 0 0 0 1 1 0 0 0 | 1 1 0 1 0
..x ... ...     | 0  0  2 | * *  * * *  * 8 * * | 0 1 0 0 0 0 0 1 1 0 | 1 1 0 0 1
... ..x ...     | 0  0  2 | * *  * * *  * * 8 * | 0 0 0 0 0 1 0 1 0 1 | 1 0 0 1 1
... ... ..x     | 0  0  2 | * *  * * *  * * * 8 | 0 0 0 0 0 0 1 0 1 1 | 0 1 0 1 1
----------------+---------+---------------------+---------------------+----------
... x..4x..     | 8  0  0 | 4 4  0 0 0  0 0 0 0 | 1 * * * * * * * * * | 0 0 2 0 0
ofx ... ...&#xt | 1  2  2 | 0 0  2 0 0  2 1 0 0 | * 8 * * * * * * * * | 1 1 0 0 0
... xx. ...&#x  | 2  2  0 | 1 0  2 1 0  0 0 0 0 | * * 8 * * * * * * * | 1 0 1 0 0
... ... xx.&#x  | 2  2  0 | 0 1  2 0 1  0 0 0 0 | * * * 8 * * * * * * | 0 1 1 0 0
... .x.4.x.     | 0  8  0 | 0 0  0 4 4  0 0 0 0 | * * * * 2 * * * * * | 0 0 1 1 0
... .xx ...&#x  | 0  2  2 | 0 0  0 1 0  2 0 1 0 | * * * * * 8 * * * * | 1 0 0 1 0
... ... .xx&#x  | 0  2  2 | 0 0  0 0 1  2 0 0 1 | * * * * * * 8 * * * | 0 1 0 1 0
..x ..x ...     | 0  0  4 | 0 0  0 0 0  0 2 2 0 | * * * * * * * 4 * * | 1 0 0 0 1
..x ... ..x     | 0  0  4 | 0 0  0 0 0  0 2 0 2 | * * * * * * * * 4 * | 0 1 0 0 1
... ..x4..x     | 0  0  8 | 0 0  0 0 0  0 0 4 4 | * * * * * * * * * 2 | 0 0 0 1 1
----------------+---------+---------------------+---------------------+----------
ofx xxx ...&#xt ♦ 2  4  4 | 1 0  4 2 0  4 2 2 0 | 0 2 2 0 0 2 0 1 0 0 | 4 * * * *
ofx ... xxx&#xt ♦ 2  4  4 | 0 1  4 0 2  4 2 0 2 | 0 2 0 2 0 0 2 0 1 0 | * 4 * * *
... xx.4xx.&#x  ♦ 8  8  0 | 4 4  8 4 4  0 0 0 0 | 1 0 4 4 1 0 0 0 0 0 | * * 2 * *
... .xx4.xx&#x  ♦ 0  8  8 | 0 0  0 4 4  8 0 4 4 | 0 0 0 0 1 4 4 0 0 1 | * * * 2 *
..x ..x4..x     ♦ 0  0 16 | 0 0  0 0 0  0 8 8 8 | 0 0 0 0 0 0 0 4 4 2 | * * * * 1