Acronym squipdip, K-4.42
Name square-pentagon duoprism
 
 
 ©
Circumradius sqrt[(10+sqrt(5))/10] = 1.106168
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {4} between cube and cube:   108°
  • at {4} between cube and pip:   90°
  • at {5} between pip and pip:   90°
Confer
general duoprisms:
4,n-dip   5,n-dip   n,m-dip   2n,m-dip  
general polytopal classes:
segmentochora   bistratic lace towers  
External
links
hedrondude   wikipedia

Incidence matrix according to Dynkin symbol

x4o x5o

. . . . | 20 |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 20  * | 1  2 0 | 2 1
. . x . |  2 |  * 20 | 0  2 1 | 1 2
--------+----+-------+--------+----
x4o . . |  4 |  4  0 | 5  * * | 2 0
x . x . |  4 |  2  2 | * 20 * | 1 1
. . x5o |  5 |  0  5 | *  * 4 | 0 2
--------+----+-------+--------+----
x4o x .   8 |  8  4 | 2  4 0 | 5 *
x . x5o  10 |  5 10 | 0  5 2 | * 4

x4o x5/4o

. . .   . | 20 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 20  * | 1  2 0 | 2 1
. . x   . |  2 |  * 20 | 0  2 1 | 1 2
----------+----+-------+--------+----
x4o .   . |  4 |  4  0 | 5  * * | 2 0
x . x   . |  4 |  2  2 | * 20 * | 1 1
. . x5/4o |  5 |  0  5 | *  * 4 | 0 2
----------+----+-------+--------+----
x4o x   .   8 |  8  4 | 2  4 0 | 5 *
x . x5/4o  10 |  5 10 | 0  5 2 | * 4

x4/3o x5o

.   . . . | 20 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x   . . . |  2 | 20  * | 1  2 0 | 2 1
.   . x . |  2 |  * 20 | 0  2 1 | 1 2
----------+----+-------+--------+----
x4/3o . . |  4 |  4  0 | 5  * * | 2 0
x   . x . |  4 |  2  2 | * 20 * | 1 1
.   . x5o |  5 |  0  5 | *  * 4 | 0 2
----------+----+-------+--------+----
x4/3o x .   8 |  8  4 | 2  4 0 | 5 *
x   . x5o  10 |  5 10 | 0  5 2 | * 4

x4/3o x5/4o

.   . .   . | 20 |  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 20  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 20 | 0  2 1 | 1 2
------------+----+-------+--------+----
x4/3o .   . |  4 |  4  0 | 5  * * | 2 0
x   . x   . |  4 |  2  2 | * 20 * | 1 1
.   . x5/4o |  5 |  0  5 | *  * 4 | 0 2
------------+----+-------+--------+----
x4/3o x   .   8 |  8  4 | 2  4 0 | 5 *
x   . x5/4o  10 |  5 10 | 0  5 2 | * 4

x x x5o

. . . . | 20 |  1  1  2 | 1  2  2 1 | 2 1 1
--------+----+----------+-----------+------
x . . . |  2 | 10  *  * | 1  2  0 0 | 2 1 0
. x . . |  2 |  * 10  * | 1  0  2 0 | 2 0 1
. . x . |  2 |  *  * 20 | 0  1  1 1 | 1 1 1
--------+----+----------+-----------+------
x x . . |  4 |  2  2  0 | 5  *  * * | 2 0 0
x . x . |  4 |  2  0  2 | * 10  * * | 1 1 0
. x x . |  4 |  0  2  2 | *  * 10 * | 1 0 1
. . x5o |  5 |  0  0  5 | *  *  * 4 | 0 1 1
--------+----+----------+-----------+------
x x x .   8 |  4  4  4 | 2  2  2 0 | 5 * *
x . x5o  10 |  5  0 10 | 0  5  0 2 | * 2 *
. x x5o  10 |  0  5 10 | 0  0  5 2 | * * 2

xx xx5oo&#x   → height = 1
(pip || pip)

o. o.5o.    | 10  * | 1  2  1 0  0 | 2 1 1  2 0 0 | 1 2 1 0
.o .o5.o    |  * 10 | 0  0  1 1  2 | 0 0 1  2 2 1 | 0 2 1 1
------------+-------+--------------+--------------+--------
x. .. ..    |  2  0 | 5  *  * *  * | 2 0 1  0 0 0 | 1 2 0 0
.. x. ..    |  2  0 | * 10  * *  * | 1 1 0  1 0 0 | 1 1 1 0
oo oo5oo&#x |  1  1 | *  * 10 *  * | 0 0 1  2 0 0 | 0 2 1 0
.x .. ..    |  0  2 | *  *  * 5  * | 0 0 1  0 2 0 | 0 2 0 1
.. .x ..    |  0  2 | *  *  * * 10 | 0 0 0  1 1 1 | 0 1 1 1
------------+-------+--------------+--------------+--------
x. x. ..    |  4  0 | 2  2  0 0  0 | 5 * *  * * * | 1 1 0 0
.. x.5o.    |  5  0 | 0  5  0 0  0 | * 2 *  * * * | 1 0 1 0
xx .. ..&#x |  2  2 | 1  0  2 1  0 | * * 5  * * * | 0 2 0 0
.. xx ..&#x |  2  2 | 0  1  2 0  1 | * * * 10 * * | 0 1 1 0
.x .x ..    |  0  4 | 0  0  0 2  2 | * * *  * 5 * | 0 1 0 1
.. .x5.o    |  0  5 | 0  0  0 0  5 | * * *  * * 2 | 0 0 1 1
------------+-------+--------------+--------------+--------
x. x.5o.     10  0 | 5 10  0 0  0 | 5 2 0  0 0 0 | 1 * * *
xx xx ..&#x   4  4 | 2  2  4 2  2 | 1 0 2  2 1 0 | * 5 * *
.. xx5oo&#x   5  5 | 0  5  5 0  5 | 0 1 0  5 0 1 | * * 2 *
.x .x5.o      0 10 | 0  0  0 5 10 | 0 0 0  0 5 2 | * * * 1

ofx xxx4ooo&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
                    height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057
({4} || pseudo (f,x,x)-cube || cube)

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

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

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

oqo xxx5ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
({5} || pseudo (q,x)-pip || {5})

o.. o..5o..     & | 10  * |  2  2  0 | 1 1  4 0 | 2 2
.o. .o.5.o.       |  * 10 |  0  2  2 | 0 1  4 1 | 2 2
------------------+-------+----------+----------+----
... x.. ...     & |  2  0 | 10  *  * | 1 0  2 0 | 1 2
oo. oo.5oo.&#x  & |  1  1 |  * 20  * | 0 1  2 0 | 2 1
... .x. ...       |  0  2 |  *  * 10 | 0 0  2 1 | 1 2
------------------+-------+----------+----------+----
... x..5o..     & |  5  0 |  5  0  0 | 2 *  * * | 0 2
oqo ... ...&#xt   |  2  2 |  0  4  0 | * 5  * * | 2 0
... xx. ...&#x  & |  2  2 |  1  2  1 | * * 20 * | 1 1
... .x.5.o.       |  0  5 |  0  0  5 | * *  * 2 | 0 2
------------------+-------+----------+----------+----
oqo xxx ...&#xt     4  4 |  2  8  2 | 0 2  4 0 | 5 *
... xx.5oo.&#x  &   5  5 |  5  5  5 | 1 0  5 1 | * 4

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