Acronym trapedip, K-4.34
Name triangle - pentagon duoprism,
pentagon - pip wedge
 
 
 ©
Circumradius sqrt[(25+3 sqrt(5))/30] = 1.028076
Volume sqrt[75+30 sqrt(5)]/16 = 0.744989
General of army (is itself convex)
Colonel of regiment (is itself locally convex)
Dihedral angles
  • at {3} between trip and trip:   108°
  • at {4} between pip and trip:   90°
  • at {5} between pip and pip:   60°
Confer
general duoprisms:
n,m-dip   3,n-dip   5,n-dip  
general polytopal classes:
segmentochora   bistratic lace towers  
External
links
hedrondude   wikipedia   polytopewiki

As abstract polytope trapedip is isomorphic to tistadip, thereby replacing pentagons by pentagrams, resp. pip by stip.


Incidence matrix according to Dynkin symbol

x3o x5o

. . . . | 15 |  2  2 | 1  4 1 | 2 2
--------+----+-------+--------+----
x . . . |  2 | 15  * | 1  2 0 | 2 1
. . x . |  2 |  * 15 | 0  2 1 | 1 2
--------+----+-------+--------+----
x3o . . |  3 |  3  0 | 5  * * | 2 0
x . x . |  4 |  2  2 | * 15 * | 1 1
. . x5o |  5 |  0  5 | *  * 3 | 0 2
--------+----+-------+--------+----
x3o x .   6 |  6  3 | 2  3 0 | 5 *
x . x5o  10 |  5 10 | 0  5 2 | * 3

x3o x5/4o

. . .   . | 15 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x . .   . |  2 | 15  * | 1  2 0 | 2 1
. . x   . |  2 |  * 15 | 0  2 1 | 1 2
----------+----+-------+--------+----
x3o .   . |  3 |  3  0 | 5  * * | 2 0
x . x   . |  4 |  2  2 | * 15 * | 1 1
. . x5/4o |  5 |  0  5 | *  * 3 | 0 2
----------+----+-------+--------+----
x3o x   .   6 |  6  3 | 2  3 0 | 5 *
x . x5/4o  10 |  5 10 | 0  5 2 | * 3

x3/2o x5o

.   . . . | 15 |  2  2 | 1  4 1 | 2 2
----------+----+-------+--------+----
x   . . . |  2 | 15  * | 1  2 0 | 2 1
.   . x . |  2 |  * 15 | 0  2 1 | 1 2
----------+----+-------+--------+----
x3/2o . . |  3 |  3  0 | 5  * * | 2 0
x   . x . |  4 |  2  2 | * 15 * | 1 1
.   . x5o |  5 |  0  5 | *  * 3 | 0 2
----------+----+-------+--------+----
x3/2o x .   6 |  6  3 | 2  3 0 | 5 *
x   . x5o  10 |  5 10 | 0  5 2 | * 3

x3/2o x5/4o

.   . .   . | 15 |  2  2 | 1  4 1 | 2 2
------------+----+-------+--------+----
x   . .   . |  2 | 15  * | 1  2 0 | 2 1
.   . x   . |  2 |  * 15 | 0  2 1 | 1 2
------------+----+-------+--------+----
x3/2o .   . |  3 |  3  0 | 5  * * | 2 0
x   . x   . |  4 |  2  2 | * 15 * | 1 1
.   . x5/4o |  5 |  0  5 | *  * 3 | 0 2
------------+----+-------+--------+----
x3/2o x   .   6 |  6  3 | 2  3 0 | 5 *
x   . x5/4o  10 |  5 10 | 0  5 2 | * 3

ox xx5oo&#x    → height = sqrt(3)/2 = 0.866025
({5} || pip)

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

ofx xxx3ooo&#xt   → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785
                    height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057

o.. o..3o..     | 3 * * | 2 2 0 0 0 0 | 1 1 4 0 0 0 0 | 2 2 0 0
.o. .o.3.o.     | * 6 * | 0 1 2 1 0 0 | 0 1 2 1 2 0 0 | 2 1 1 0
..o ..o3..o     | * * 6 | 0 0 0 1 1 2 | 0 1 0 0 2 2 1 | 2 0 1 1
----------------+-------+-------------+---------------+--------
... x.. ...     | 2 0 0 | 3 * * * * * | 1 0 2 0 0 0 0 | 1 2 0 0
oo. oo.3oo.&#x  | 1 1 0 | * 6 * * * * | 0 1 2 0 0 0 0 | 2 1 0 0
... .x. ...     | 0 2 0 | * * 6 * * * | 0 0 1 1 1 0 0 | 1 1 1 0
.oo .oo3.oo&#x  | 0 1 1 | * * * 6 * * | 0 1 0 0 2 0 0 | 2 0 1 0
..x ... ...     | 0 0 2 | * * * * 3 * | 0 1 0 0 0 2 0 | 2 0 0 1
... ..x ...     | 0 0 2 | * * * * * 6 | 0 0 0 0 1 1 1 | 1 0 1 1
----------------+-------+-------------+---------------+--------
... x..3o..     | 3 0 0 | 3 0 0 0 0 0 | 1 * * * * * * | 0 2 0 0
ofx ... ...&#xt | 1 2 2 | 0 2 0 2 1 0 | * 3 * * * * * | 2 0 0 0
... xx. ...&#x  | 2 2 0 | 1 2 1 0 0 0 | * * 6 * * * * | 1 1 0 0
... .x.3.o.     | 0 3 0 | 0 0 3 0 0 0 | * * * 2 * * * | 0 1 1 0
... .xx ...&#x  | 0 2 2 | 0 0 1 2 0 1 | * * * * 6 * * | 1 0 1 0
..x ..x ...     | 0 0 4 | 0 0 0 0 2 2 | * * * * * 3 * | 1 0 0 1
... ..x3..o     | 0 0 3 | 0 0 0 0 0 3 | * * * * * * 2 | 0 0 1 1
----------------+-------+-------------+---------------+--------
ofx xxx ...&#xt  2 4 4 | 1 4 2 4 2 2 | 0 2 2 0 2 1 0 | 3 * * *
... xx.3oo.&#x   3 3 0 | 3 3 3 0 0 0 | 1 0 3 1 0 0 0 | * 2 * *
... .xx3.oo&#x   0 3 3 | 0 0 3 3 0 3 | 0 0 0 1 3 0 1 | * * 2 *
..x ..x3..o      0 0 6 | 0 0 0 0 3 6 | 0 0 0 0 0 3 2 | * * * 1

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