Acronym dope, K-4.74
Name dodecahedron prism
Segmentochoron display
Cross sections
 ©
Circumradius sqrt[(11+3 sqrt(5))/8] = 1.487792
Coordinates
  1. (τ/2, τ/2, τ/2, 1/2)   & all permutations in all but last coord., all changes of sign
    (vertex inscribed f-cube)
  2. 2/2, 1/2, 0, 1/2)   & even permutations, all changes of sign
where τ = (1+sqrt(5))/2
General of army (is itself convex)
Colonel of regiment (is itself locally convex – no other uniform polychoral members)
Dual ikedpy
Dihedral angles
  • at {4} between pip and pip:   arccos(-1/sqrt(5)) = 116.565051°
  • at {5} between doe and pip:   90°
Confer
decompositions:
ike || dope  
general polytopal classes:
segmentochora  
External
links
hedrondude   wikipedia

As abstract polytope dope is isomorphic to gissiddip, thereby replacing pentagons by pentagrams resp. replacing doe by gissid and pip by stip.

Note that dope can be thought of as the external blend of 20 pens + 30 squascs + 12 pippies + 2 ikadoes. This decomposition is described as the degenerate segmentoteron ox xo3oo5ox&#x.


Incidence matrix according to Dynkin symbol

x o3o5x

. . . . | 40 |  1  3 |  3  3 |  3 1
--------+----+-------+-------+-----
x . . . |  2 | 20  * |  3  0 |  3 0
. . . x |  2 |  * 60 |  1  2 |  2 1
--------+----+-------+-------+-----
x . . x |  4 |  2  2 | 30  * |  2 0
. . o5x |  5 |  0  5 |  * 24 |  1 1
--------+----+-------+-------+-----
x . o5x  10 |  5 10 |  5  2 | 12 *
. o3o5x  20 |  0 30 |  0 12 |  * 2

snubbed forms: β2o3o5β

x o3o5/4x

. . .   . | 40 |  1  3 |  3  3 |  3 1
----------+----+-------+-------+-----
x . .   . |  2 | 20  * |  3  0 |  3 0
. . .   x |  2 |  * 60 |  1  2 |  2 1
----------+----+-------+-------+-----
x . .   x |  4 |  2  2 | 30  * |  2 0
. . o5/4x |  5 |  0  5 |  * 24 |  1 1
----------+----+-------+-------+-----
x . o5/4x  10 |  5 10 |  5  2 | 12 *
. o3o5/4x  20 |  0 30 |  0 12 |  * 2

x o3/2o5x

. .   . . | 40 |  1  3 |  3  3 |  3 1
----------+----+-------+-------+-----
x .   . . |  2 | 20  * |  3  0 |  3 0
. .   . x |  2 |  * 60 |  1  2 |  2 1
----------+----+-------+-------+-----
x .   . x |  4 |  2  2 | 30  * |  2 0
. .   o5x |  5 |  0  5 |  * 24 |  1 1
----------+----+-------+-------+-----
x .   o5x  10 |  5 10 |  5  2 | 12 *
. o3/2o5x  20 |  0 30 |  0 12 |  * 2

x o3/2o5/4x

. .   .   . | 40 |  1  3 |  3  3 |  3 1
------------+----+-------+-------+-----
x .   .   . |  2 | 20  * |  3  0 |  3 0
. .   .   x |  2 |  * 60 |  1  2 |  2 1
------------+----+-------+-------+-----
x .   .   x |  4 |  2  2 | 30  * |  2 0
. .   o5/4x |  5 |  0  5 |  * 24 |  1 1
------------+----+-------+-------+-----
x .   o5/4x  10 |  5 10 |  5  2 | 12 *
. o3/2o5/4x  20 |  0 30 |  0 12 |  * 2

oo3oo5xx&#x   → height = 1
(doe || doe)

o.3o.5o.    | 20  * |  3  1  0 |  3  3  0 | 1  3 0
.o3.o5.o    |  * 20 |  0  1  3 |  0  3  3 | 0  3 1
------------+-------+----------+----------+-------
.. .. x.    |  2  0 | 30  *  * |  2  1  0 | 1  2 0
oo3oo5oo&#x |  1  1 |  * 20  * |  0  3  0 | 0  3 0
.. .. .x    |  0  2 |  *  * 30 |  0  1  2 | 0  2 1
------------+-------+----------+----------+-------
.. o.5x.    |  5  0 |  5  0  0 | 12  *  * | 1  1 0
.. .. xx&#x |  2  2 |  1  2  1 |  * 30  * | 0  2 0
.. .o5.x    |  0  5 |  0  0  5 |  *  * 12 | 0  1 1
------------+-------+----------+----------+-------
o.3o.5x.     20  0 | 30  0  0 | 12  0  0 | 1  * *
.. oo5xx&#x   5  5 |  5  5  5 |  1  5  1 | * 12 *
.o3.o5.x      0 20 |  0  0 30 |  0  0 12 | *  * 1

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