Acronym	rap (old: rip), K-4.5
Name	rectified pentachoron, tetrahedral cupola
Segmentochoron display
Cross sections	©
Circumradius	sqrt(3/5) = 0.774597
Vertex figure	©
Vertex layers	Layer Symmetry Subsymmetries   o3o3o3o o3o3o . o3o . o o . o3o . o3o3o 1 o3x3o3o o3x3o . oct first o3x . o {3} first o . o3o vertex first . x3o3o tet first 2 x3o3o . opposite tet x3o . x x . x3o vertex figure . o3x3o opposite oct 3   o3o . o opposite vertex o . o3x opposite {3}
Lace city in approx. ASCII-art	o3o x3o x3o o3x
	x o o x o o x x o o
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: oct tet trip rap 5 5 0 pinnip 5 0 10 firp 0 5 10 )
Confer	Grünbaumian relatives: firp+rap+15{4}   2rap   2rap+20tet   segmentochora: trippy   {3} || gyro trip
External links

Incidence matrix according to Dynkin symbol

o3x3o3o

. . . . | 10 ♦  6 |  3  6 | 3 2
--------+----+----+-------+----
. x . . |  2 | 30 |  1  2 | 2 1
--------+----+----+-------+----
o3x . . |  3 |  3 | 10  * | 2 0
. x3o . |  3 |  3 |  * 20 | 1 1
--------+----+----+-------+----
o3x3o . ♦  6 | 12 |  4  4 | 5 *
. x3o3o ♦  4 |  6 |  0  4 | * 5

o3x3o3/2o

. . .   . | 10 ♦  6 |  3  6 | 3 2
----------+----+----+-------+----
. x .   . |  2 | 30 |  1  2 | 2 1
----------+----+----+-------+----
o3x .   . |  3 |  3 | 10  * | 2 0
. x3o   . |  3 |  3 |  * 20 | 1 1
----------+----+----+-------+----
o3x3o   . ♦  6 | 12 |  4  4 | 5 *
. x3o3/2o ♦  4 |  6 |  0  4 | * 5

o3x3/2o3o

. .   . . | 10 ♦  6 |  3  6 | 3 2
----------+----+----+-------+----
. x   . . |  2 | 30 |  1  2 | 2 1
----------+----+----+-------+----
o3x   . . |  3 |  3 | 10  * | 2 0
. x3/2o . |  3 |  3 |  * 20 | 1 1
----------+----+----+-------+----
o3x3/2o . ♦  6 | 12 |  4  4 | 5 *
. x3/2o3o ♦  4 |  6 |  0  4 | * 5

o3x3/2o3/2o

. .   .   . | 10 ♦  6 |  3  6 | 3 2
------------+----+----+-------+----
. x   .   . |  2 | 30 |  1  2 | 2 1
------------+----+----+-------+----
o3x   .   . |  3 |  3 | 10  * | 2 0
. x3/2o   . |  3 |  3 |  * 20 | 1 1
------------+----+----+-------+----
o3x3/2o   . ♦  6 | 12 |  4  4 | 5 *
. x3/2o3/2o ♦  4 |  6 |  0  4 | * 5

o3/2x3o3o

.   . . . | 10 ♦  6 |  3  6 | 3 2
----------+----+----+-------+----
.   x . . |  2 | 30 |  1  2 | 2 1
----------+----+----+-------+----
o3/2x . . |  3 |  3 | 10  * | 2 0
.   x3o . |  3 |  3 |  * 20 | 1 1
----------+----+----+-------+----
o3/2x3o . ♦  6 | 12 |  4  4 | 5 *
.   x3o3o ♦  4 |  6 |  0  4 | * 5

o3/2x3o3/2o

.   . .   . | 10 ♦  6 |  3  6 | 3 2
------------+----+----+-------+----
.   x .   . |  2 | 30 |  1  2 | 2 1
------------+----+----+-------+----
o3/2x .   . |  3 |  3 | 10  * | 2 0
.   x3o   . |  3 |  3 |  * 20 | 1 1
------------+----+----+-------+----
o3/2x3o   . ♦  6 | 12 |  4  4 | 5 *
.   x3o3/2o ♦  4 |  6 |  0  4 | * 5

o3/2x3/2o3o

.   .   . . | 10 ♦  6 |  3  6 | 3 2
------------+----+----+-------+----
.   x   . . |  2 | 30 |  1  2 | 2 1
------------+----+----+-------+----
o3/2x   . . |  3 |  3 | 10  * | 2 0
.   x3/2o . |  3 |  3 |  * 20 | 1 1
------------+----+----+-------+----
o3/2x3/2o . ♦  6 | 12 |  4  4 | 5 *
.   x3/2o3o ♦  4 |  6 |  0  4 | * 5

o3/2x3/2o3/2o

.   .   .   . | 10 ♦  6 |  3  6 | 3 2
--------------+----+----+-------+----
.   x   .   . |  2 | 30 |  1  2 | 2 1
--------------+----+----+-------+----
o3/2x   .   . |  3 |  3 | 10  * | 2 0
.   x3/2o   . |  3 |  3 |  * 20 | 1 1
--------------+----+----+-------+----
o3/2x3/2o   . ♦  6 | 12 |  4  4 | 5 *
.   x3/2o3/2o ♦  4 |  6 |  0  4 | * 5

xo3ox3oo&#x   → height = sqrt(5/8) = 0.790569
(tet || oct)

o.3o.3o.    | 4 * ♦ 3  3  0 | 3 3  3 0 0 | 1 3 1 0
.o3.o3.o    | * 6 ♦ 0  2  4 | 0 1  4 2 2 | 0 2 2 1
------------+-----+---------+------------+--------
x. .. ..    | 2 0 | 6  *  * | 2 1  0 0 0 | 1 2 0 0
oo3oo3oo&#x | 1 1 | * 12  * | 0 1  2 0 0 | 0 2 1 0
.. .x ..    | 0 2 | *  * 12 | 0 0  1 1 1 | 0 1 1 1
------------+-----+---------+------------+--------
x.3o. ..    | 3 0 | 3  0  0 | 4 *  * * * | 1 1 0 0
xo .. ..&#x | 2 1 | 1  2  0 | * 6  * * * | 0 2 0 0
.. ox ..&#x | 1 2 | 0  2  1 | * * 12 * * | 0 1 1 0
.o3.x ..    | 0 3 | 0  0  3 | * *  * 4 * | 0 1 0 1
.. .x3.o    | 0 3 | 0  0  3 | * *  * * 4 | 0 0 1 1
------------+-----+---------+------------+--------
x.3o.3o.    ♦ 4 0 | 6  0  0 | 4 0  0 0 0 | 1 * * *
xo3ox ..&#x ♦ 3 3 | 3  6  3 | 1 3  3 1 0 | * 4 * *
.. ox3oo&#x ♦ 1 3 | 0  3  3 | 0 0  3 0 1 | * * 4 *
.o3.x3.o    ♦ 0 6 | 0  0 12 | 0 0  0 4 4 | * * * 1

oxo oxo3oox&#xt   → both heights = sqrt(5/12) = 0.645497
(pt || pseudo trip || dual {3})

o.. o..3o..     | 1 * * ♦ 6 0 0  0 0 | 3 6 0 0 0 0 0 | 3 2 0 0
.o. .o.3.o.     | * 6 * ♦ 1 1 2  2 0 | 1 2 1 2 2 1 0 | 2 1 1 1
..o ..o3..o     | * * 3 ♦ 0 0 0  4 2 | 0 0 0 2 2 4 1 | 1 0 2 2
----------------+-------+------------+---------------+--------
oo. oo.3oo.&#x  | 1 1 0 | 6 * *  * * | 1 2 0 0 0 0 0 | 2 1 0 0
.x. ... ...     | 0 2 0 | * 3 *  * * | 1 0 0 2 0 0 0 | 2 0 1 0
... .x. ...     | 0 2 0 | * * 6  * * | 0 1 1 0 1 0 0 | 1 1 0 1
.oo .oo3.oo&#x  | 0 1 1 | * * * 12 * | 0 0 0 1 1 1 0 | 1 0 1 1
... ... ..x     | 0 0 2 | * * *  * 3 | 0 0 0 0 0 2 1 | 0 0 1 2
----------------+-------+------------+---------------+--------
ox. ... ...&#x  | 1 2 0 | 2 1 0  0 0 | 3 * * * * * * | 2 0 0 0
... ox. ...&#x  | 1 2 0 | 2 0 1  0 0 | * 6 * * * * * | 1 1 0 0
... .x.3.o.     | 0 3 0 | 0 0 3  0 0 | * * 2 * * * * | 0 1 0 1
.xo ... ...&#x  | 0 2 1 | 0 1 0  2 0 | * * * 6 * * * | 1 0 1 0
... .xo ...&#x  | 0 2 1 | 0 0 1  2 0 | * * * * 6 * * | 1 0 0 1
... ... .ox&#x  | 0 1 2 | 0 0 0  2 1 | * * * * * 6 * | 0 0 1 1
... ..o3..x     | 0 0 3 | 0 0 0  0 3 | * * * * * * 1 | 0 0 0 2
----------------+-------+------------+---------------+--------
oxo oxo ...&#xt ♦ 1 4 1 | 4 2 2  4 0 | 2 2 0 2 2 0 0 | 3 * * *
... ox.3oo.&#x  ♦ 1 3 0 | 3 0 3  0 0 | 0 3 1 0 0 0 0 | * 2 * *
.xo ... .ox&#x  ♦ 0 2 2 | 0 1 0  4 1 | 0 0 0 2 0 2 0 | * * 3 *
... .xo3.ox&#x  ♦ 0 3 3 | 0 0 3  6 3 | 0 0 1 0 3 3 1 | * * * 2

oxoo3xoxo&#xr   → all heights = sqrt(2/3) = 0.816497
({3} || pseudo (dual {3} || pt) || {3}

o...3o...     | 3 * * * ♦ 2 2 1 1 0 0 0 0 | 1 1 2 2 2 1 0 0 0 0 0 | 1 1 1 2 0 0
.o..3.o..     | * 3 * * ♦ 0 2 0 0 2 2 0 0 | 0 2 1 0 2 0 1 2 1 0 0 | 1 0 2 1 1 0
..o.3..o.     | * * 3 * ♦ 0 0 1 0 0 2 2 1 | 0 0 0 0 2 1 0 1 2 1 2 | 0 0 1 2 1 1
...o3...o     | * * * 1 ♦ 0 0 0 3 0 0 0 3 | 0 0 0 3 0 3 0 0 0 0 3 | 0 1 0 3 0 1
--------------+---------+-----------------+-----------------------+------------
.... x...     | 2 0 0 0 | 3 * * * * * * * | 1 0 1 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
oo..3oo..&#x  | 1 1 0 0 | * 6 * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
o.o.3o.o.&#x  | 1 0 1 0 | * * 3 * * * * * | 0 0 0 0 2 1 0 0 0 0 0 | 0 0 1 2 0 0
o..o3o..o&#x  | 1 0 0 1 | * * * 3 * * * * | 0 0 0 2 0 1 0 0 0 0 0 | 0 1 0 2 0 0
.x.. ....     | 0 2 0 0 | * * * * 3 * * * | 0 1 0 0 0 0 1 1 0 0 0 | 1 0 1 0 1 0
.oo.3.oo.&#x  | 0 1 1 0 | * * * * * 6 * * | 0 0 0 0 1 0 0 1 1 0 0 | 0 0 1 1 1 0
.... ..x.     | 0 0 2 0 | * * * * * * 3 * | 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1
..oo3..oo&#x  | 0 0 1 1 | * * * * * * * 3 | 0 0 0 0 0 1 0 0 0 0 2 | 0 0 0 2 0 1
--------------+---------+-----------------+-----------------------+------------
o...3x...     | 3 0 0 0 | 3 0 0 0 0 0 0 0 | 1 * * * * * * * * * * | 1 1 0 0 0 0
ox.. ....&#x  | 1 2 0 0 | 0 2 0 0 1 0 0 0 | * 3 * * * * * * * * * | 1 0 1 0 0 0
.... xo..&#x  | 2 1 0 0 | 1 2 0 0 0 0 0 0 | * * 3 * * * * * * * * | 1 0 0 1 0 0
.... x..o&#x  | 2 0 0 1 | 1 0 0 2 0 0 0 0 | * * * 3 * * * * * * * | 0 1 0 1 0 0
ooo.3ooo.&#x  | 1 1 1 0 | 0 1 1 0 0 1 0 0 | * * * * 6 * * * * * * | 0 0 1 1 0 0
o.oo3o.oo&#x  | 1 0 1 1 | 0 0 1 1 0 0 0 1 | * * * * * 3 * * * * * | 0 0 0 2 0 0
.x..3.o..     | 0 3 0 0 | 0 0 0 0 3 0 0 0 | * * * * * * 1 * * * * | 1 0 0 0 1 0
.xo. ....&#x  | 0 2 1 0 | 0 0 0 0 1 2 0 0 | * * * * * * * 3 * * * | 0 0 1 0 1 0
.... .ox.&#x  | 0 1 2 0 | 0 0 0 0 0 2 1 0 | * * * * * * * * 3 * * | 0 0 0 1 1 0
..o.3..x.     | 0 0 3 0 | 0 0 0 0 0 0 3 0 | * * * * * * * * * 1 * | 0 0 0 0 1 1
.... ..xo&#x  | 0 0 2 1 | 0 0 0 0 0 0 1 2 | * * * * * * * * * * 3 | 0 0 0 1 0 1
--------------+---------+-----------------+-----------------------+------------
ox..3xo..&#x  ♦ 3 3 0 0 | 3 6 0 0 3 0 0 0 | 1 3 3 0 0 0 1 0 0 0 0 | 1 * * * * *
o..o3x..o&#x  ♦ 3 0 0 1 | 3 0 0 3 0 0 0 0 | 1 0 0 3 0 0 0 0 0 0 0 | * 1 * * * *
oxo. ....&#x  ♦ 1 2 1 0 | 0 2 1 0 1 2 0 0 | 0 1 0 0 2 0 0 1 0 0 0 | * * 3 * * *
.... xoxo&#xr ♦ 2 1 2 1 | 1 2 2 2 0 2 1 2 | 0 0 1 1 2 2 0 0 1 0 1 | * * * 3 * *
.xo.3.ox.&#x  ♦ 0 3 3 0 | 0 0 0 0 3 6 3 0 | 0 0 0 0 0 0 1 3 3 1 0 | * * * * 1 *
..oo3..xo&#x  ♦ 0 0 3 1 | 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 0 1 3 | * * * * * 1