Acronym rin
Name rectified penteract
Field of sections
 ©
Circumradius sqrt(2) = 1.414214
Vertex figure
 ©    ©
Lace city
in approx. ASCII-art
o3x4o  o3o4q  o3x4o		-- o3o3x4o (rit)
                   
                   
                   
o3o4q         o3o4q		-- o3o3o4q (q-tes)
                   
                   
                   
o3x4o  o3o4q  o3x4o		-- o3o3x4o (rit)
         +----------	o3o3x4o (rit)
        /    +------	o3o3o4q (q-tes)
       /    /     +-	o3o3x4o (rit)
                 / 
   x3o3o o3o3o     		-- x3o3o3o (pen)
                   
  x3x3o u3o3o x3o3o		-- x3x3o3o (tip)
                   
 o3x3x o3u3o x3x3o 		-- o3x3x3o (deca)
                   
o3o3x o3o3u o3x3x  		-- o3o3x3x (alt. tip)
                   
     o3o3o o3o3x   		-- o3o3o3x (dual pen)
Coordinates (1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0)   & all permutations, all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
by cells: firt pen rit tip
tin 100032
rin 032100
& others)
Confer
related segmentotera:
pennatip   tipadeca  
general polytopal classes:
partial Stott expansions  
External
links
hedrondude   wikipedia  

Incidence matrix according to Dynkin symbol

o3o3o3x4o

. . . . . | 80    8 |  12  4 |   8  6 |  2  4
----------+----+-----+--------+--------+------
. . . x . |  2 | 320 |   3  1 |   3  3 |  1  3
----------+----+-----+--------+--------+------
. . o3x . |  3 |   3 | 320  * |   2  1 |  1  2
. . . x4o |  4 |   4 |   * 80 |   0  3 |  0  3
----------+----+-----+--------+--------+------
. o3o3x .   4 |   6 |   4  0 | 160  * |  1  1
. . o3x4o  12 |  24 |   8  6 |   * 40 |  0  2
----------+----+-----+--------+--------+------
o3o3o3x .   5 |  10 |  10  0 |   5  0 | 32  *
. o3o3x4o  32 |  96 |  64 24 |  16  8 |  * 10

o3o3o3x4/3o

. . . .   . | 80    8 |  12  4 |   8  6 |  2  4
------------+----+-----+--------+--------+------
. . . x   . |  2 | 320 |   3  1 |   3  3 |  1  3
------------+----+-----+--------+--------+------
. . o3x   . |  3 |   3 | 320  * |   2  1 |  1  2
. . . x4/3o |  4 |   4 |   * 80 |   0  3 |  0  3
------------+----+-----+--------+--------+------
. o3o3x   .   4 |   6 |   4  0 | 160  * |  1  1
. . o3x4/3o  12 |  24 |   8  6 |   * 40 |  0  2
------------+----+-----+--------+--------+------
o3o3o3x   .   5 |  10 |  10  0 |   5  0 | 32  *
. o3o3x4/3o  32 |  96 |  64 24 |  16  8 |  * 10

x3o3x *b3o3o

. . .    . . | 80    4   4 |   6  4   6 |  6  4  4 |  4  1  1
-------------+----+---------+------------+----------+---------
x . .    . . |  2 | 160   * |   3  1   0 |  3  3  0 |  3  1  0
. . x    . . |  2 |   * 160 |   0  1   3 |  3  0  3 |  3  0  1
-------------+----+---------+------------+----------+---------
x3o .    . . |  3 |   3   0 | 160  *   * |  1  2  0 |  2  1  0
x . x    . . |  4 |   2   2 |   * 80   * |  3  0  0 |  3  0  0
. o3x    . . |  3 |   0   3 |   *  * 160 |  1  0  2 |  2  0  1
-------------+----+---------+------------+----------+---------
x3o3x    . .  12 |  12  12 |   4  6   4 | 40  *  * |  2  0  0
x3o . *b3o .   4 |   6   0 |   4  0   0 |  * 80  * |  1  1  0
. o3x *b3o .   4 |   0   6 |   0  0   4 |  *  * 80 |  1  0  1
-------------+----+---------+------------+----------+---------
x3o3x *b3o .  32 |  48  48 |  32 24  32 |  8  8  8 | 10  *  *
x3o . *b3o3o   5 |  10   0 |  10  0   0 |  0  5  0 |  * 16  *
. o3x *b3o3o   5 |   0  10 |   0  0  10 |  0  0  5 |  *  * 16

o3o3o3x4s

demi( . . . . . ) | 80    4   4 |   6  4   6 |  4  6  4 |  1  4  1
------------------+----+---------+------------+----------+---------
demi( . . . x . ) |  2 | 160   * |   3  1   0 |  3  3  0 |  1  3  0
sefa( . . . x4s ) |  2 |   * 160 |   0  1   3 |  0  3  3 |  0  3  1
------------------+----+---------+------------+----------+---------
demi( . . o3x . ) |  3 |   3   0 | 160  *   * |  2  1  0 |  1  2  0
      . . . x4s     4 |   2   2 |   * 80   * |  0  3  0 |  0  3  0
sefa( . . o3x4s ) |  3 |   0   3 |   *  * 160 |  0  1  2 |  0  2  1
------------------+----+---------+------------+----------+---------
demi( . o3o3x . )   4 |   6   0 |   4  0   0 | 80  *  * |  1  1  0
      . . o3x4s    12 |  12  12 |   4  6   4 |  * 40  * |  0  2  0
sefa( . o3o3x4s )   4 |   0   6 |   0  0   4 |  *  * 80 |  0  1  1
------------------+----+---------+------------+----------+---------
demi( o3o3o3x . )   5 |  10   0 |  10  0   0 |  5  0  0 | 16  *  *
      . o3o3x4s    32 |  48  48 |  32 24  32 |  8  8  8 |  * 10  *
sefa( o3o3o3x4s )   5 |   0  10 |   0  0  10 |  0  0  5 |  *  * 16

starting figure: o3o3o3x4x

ooo3ooo3xox4oqo&#xt   → both heights = 1/sqrt(2) = 0.707107
(rit || pseudo q-tes || rit)

o..3o..3o..4o..     | 32  *  *   6  2  0  0 |  6  3  6  1  0  0  0 |  2 3  6  3  0  0 0 | 1  2 3  0 0
.o.3.o.3.o.4.o.     |  * 16  *   0  4  4  0 |  0  0  6  4  6  0  0 |  0 0  4  6  4  0 0 | 0  1 4  1 0
..o3..o3..o4..o     |  *  * 32   0  0  2  6 |  0  0  0  1  6  6  3 |  0 0  0  3  6  2 3 | 0  0 3  2 1
--------------------+----------+-------------+----------------------+--------------------+------------
... ... x.. ...     |  2  0  0 | 96  *  *  * |  2  1  1  0  0  0  0 |  1 2  2  1  0  0 0 | 1  1 2  0 0
oo.3oo.3oo.4oo.&#x  |  1  1  0 |  * 64  *  * |  0  0  3  1  0  0  0 |  0 0  3  3  0  0 0 | 0  1 3  0 0
.oo3.oo3.oo4.oo&#x  |  0  1  1 |  *  * 64  * |  0  0  0  1  3  0  0 |  0 0  0  3  3  0 0 | 0  0 3  1 0
... ... ..x ...     |  0  0  2 |  *  *  * 96 |  0  0  0  0  1  2  1 |  0 0  0  1  2  1 2 | 0  0 2  1 1
--------------------+----------+-------------+----------------------+--------------------+------------
... o..3x.. ...     |  3  0  0 |  3  0  0  0 | 64  *  *  *  *  *  * |  1 1  1  0  0  0 0 | 1  1 1  0 0
... ... x..4o..     |  4  0  0 |  4  0  0  0 |  * 24  *  *  *  *  * |  0 2  0  1  0  0 0 | 1  0 2  0 0
... ... xo. ...&#x  |  2  1  0 |  1  2  0  0 |  *  * 96  *  *  *  * |  0 0  2  1  0  0 0 | 0  1 2  0 0
... ... ... oqo&#x  |  1  2  1 |  0  2  2  0 |  *  *  * 32  *  *  * |  0 0  0  3  0  0 0 | 0  0 3  0 0
... ... .ox ...&#x  |  0  1  2 |  0  0  2  1 |  *  *  *  * 96  *  * |  0 0  0  1  2  0 0 | 0  0 2  1 0
... ..o3..x ...     |  0  0  3 |  0  0  0  3 |  *  *  *  *  * 64  * |  0 0  0  0  1  1 1 | 0  0 1  1 1
... ... ..x4..o     |  0  0  4 |  0  0  0  4 |  *  *  *  *  *  * 24 |  0 0  0  1  0  0 2 | 0  0 2  0 1
--------------------+----------+-------------+----------------------+--------------------+------------
o..3o..3x.. ...       4  0  0 |  6  0  0  0 |  4  0  0  0  0  0  0 | 16 *  *  *  *  * * | 1  1 0  0 0
... o..3x..4o..      12  0  0 | 24  0  0  0 |  8  6  0  0  0  0  0 |  * 8  *  *  *  * * | 1  0 1  0 0
... oo.3xo. ...&#x    3  1  0 |  3  3  0  0 |  1  0  3  0  0  0  0 |  * * 64  *  *  * * | 0  1 1  0 0
... ... xox4oqo&#xt   4  4  4 |  4  8  8  4 |  0  1  4  4  4  0  1 |  * *  * 24  *  * * | 0  0 2  0 0
... .oo3.ox ...&#x    0  1  3 |  0  0  3  3 |  0  0  0  0  3  1  0 |  * *  *  * 64  * * | 0  0 1  1 0
..o3..o3..x ...       0  0  4 |  0  0  0  6 |  0  0  0  0  0  4  0 |  * *  *  *  * 16 * | 0  0 0  1 1
... ..o3..x4..o       0  0 12 |  0  0  0 24 |  0  0  0  0  0  8  6 |  * *  *  *  *  * 8 | 0  0 1  0 1
--------------------+----------+-------------+----------------------+--------------------+------------
o..3o..3x..4o..      32  0  0 | 96  0  0  0 | 64 24  0  0  0  0  0 | 16 8  0  0  0  0 0 | 1  * *  * *
oo.3oo.3xo. ...&#x    4  1  0 |  6  4  0  0 |  4  0  6  0  0  0  0 |  1 0  4  0  0  0 0 | * 16 *  * *
... ooo3xox4oqo&#xt  12  8 12 | 24 24 24 24 |  8  6 24 12 24  8  6 |  0 1  8  6  8  0 1 | *  * 8  * *
.oo3.oo3.ox ...&#x    0  1  4 |  0  0  4  6 |  0  0  0  0  6  4  0 |  0 0  0  0  4  1 0 | *  * * 16 *
..o3..o3..x4..o       0  0 32 |  0  0  0 96 |  0  0  0  0  0 64 24 |  0 0  0  0  0 16 8 | *  * *  * 1

xxooo3oxxoo3ooxxo3oooxx&#xt   → all heights = sqrt(2/5) = 0.632456
(pen || pseudo tip || pseudo deca || pseudo inv tip || dual pen)

o....3o....3o....3o....     & | 10  *  *   4  4  0  0   0  0 |  6  4  6  0  0  0   0  0 |  4  6  4  0  0  0  0 | 1  1  4  0
.o...3.o...3.o...3.o...     & |  * 40  *   0  1  1  3   3  0 |  0  1  3  3  3  3   3  0 |  0  3  3  1  3  3  1 | 0  1  4  1
..o..3..o..3..o..3..o..       |  *  * 30   0  0  0  0   4  4 |  0  0  0  0  2  4   8  2 |  0  2  0  0  4  4  4 | 0  0  4  2
------------------------------+----------+--------------------+--------------------------+----------------------+-----------
x.... ..... ..... .....     & |  2  0  0 | 20  *  *  *   *  * |  3  1  0  0  0  0   0  0 |  3  3  0  0  0  0  0 | 1  0  3  0
oo...3oo...3oo...3oo...&#x  & |  1  1  0 |  * 40  *  *   *  * |  0  1  3  0  0  0   0  0 |  0  3  3  0  0  0  0 | 0  1  3  0
.x... ..... ..... .....     & |  0  2  0 |  *  * 20  *   *  * |  0  1  0  0  3  0   0  0 |  0  3  0  0  3  0  0 | 0  0  3  1
..... .x... ..... .....     & |  0  2  0 |  *  *  * 60   *  * |  0  0  1  2  0  1   0  0 |  0  1  2  1  0  2  0 | 0  1  3  0
.oo..3.oo..3.oo..3.oo..&#x  & |  0  1  1 |  *  *  *  * 120  * |  0  0  0  0  1  1   2  0 |  0  1  0  0  2  2  1 | 0  0  3  1
..... ..x.. ..... .....     & |  0  0  2 |  *  *  *  *   * 60 |  0  0  0  0  0  1   2  1 |  0  1  0  0  1  2  2 | 0  0  3  1
------------------------------+----------+--------------------+--------------------------+----------------------+-----------
x....3o.... ..... .....     & |  3  0  0 |  3  0  0  0   0  0 | 20  *  *  *  *  *   *  * |  2  1  0  0  0  0  0 | 1  0  2  0
xx... ..... ..... .....&#x  & |  2  2  0 |  1  2  1  0   0  0 |  * 20  *  *  *  *   *  * |  0  3  0  0  0  0  0 | 0  0  3  0
..... ox... ..... .....&#x  & |  1  2  0 |  0  2  0  1   0  0 |  *  * 60  *  *  *   *  * |  0  1  2  0  0  0  0 | 0  1  2  0
..... .x...3.o... .....     & |  0  3  0 |  0  0  0  3   0  0 |  *  *  * 40  *  *   *  * |  0  0  1  1  0  1  0 | 0  1  2  0
.xo.. ..... ..... .....&#x  & |  0  2  1 |  0  0  1  0   2  0 |  *  *  *  * 60  *   *  * |  0  1  0  0  2  0  0 | 0  0  2  1
..... .xx.. ..... .....&#x  & |  0  2  2 |  0  0  0  1   2  1 |  *  *  *  *  * 60   *  * |  0  1  0  0  0  2  0 | 0  0  3  0
..... ..... .ox.. .....&#x  & |  0  1  2 |  0  0  0  0   2  1 |  *  *  *  *  *  * 120  * |  0  0  0  0  1  1  1 | 0  0  2  1
..o..3..x.. ..... .....     & |  0  0  3 |  0  0  0  0   0  3 |  *  *  *  *  *  *   * 20 |  0  1  0  0  0  0  2 | 0  0  2  1
------------------------------+----------+--------------------+--------------------------+----------------------+-----------
x....3o....3o.... .....     &   4  0  0 |  6  0  0  0   0  0 |  4  0  0  0  0  0   0  0 | 10  *  *  *  *  *  * | 1  0  1  0
xxo..3oxx.. ..... .....&#xt &   3  6  3 |  3  6  3  3   6  3 |  1  3  3  0  3  3   0  1 |  * 20  *  *  *  *  * | 0  0  2  0
..... ox...3oo... .....&#x  &   1  3  0 |  0  3  0  3   0  0 |  0  0  3  1  0  0   0  0 |  *  * 40  *  *  *  * | 0  1  1  0
..... .x...3.o...3.o...     &   0  4  0 |  0  0  0  6   0  0 |  0  0  0  4  0  0   0  0 |  *  *  * 10  *  *  * | 0  1  1  0
.xo.. ..... .ox.. .....&#x  &   0  2  2 |  0  0  1  0   4  1 |  0  0  0  0  2  0   2  0 |  *  *  *  * 60  *  * | 0  0  1  1
..... .xxo.3.oxx. .....&#xt     0  6  6 |  0  0  0  6  12  6 |  0  0  0  2  0  6   6  0 |  *  *  *  *  * 20  * | 0  0  2  0
..... ..... .ox..3.oo..&#x  &   0  1  3 |  0  0  0  0   3  3 |  0  0  0  0  0  0   3  1 |  *  *  *  *  *  * 40 | 0  0  1  1
------------------------------+----------+--------------------+--------------------------+----------------------+-----------
x....3o....3o....3o....     &   5  0  0 | 10  0  0  0   0  0 | 10  0  0  0  0  0   0  0 |  5  0  0  0  0  0  0 | 2  *  *  *
..... ox...3oo...3oo...&#x  &   1  4  0 |  0  4  0  6   0  0 |  0  0  6  4  0  0   0  0 |  0  0  4  1  0  0  0 | * 10  *  *
xxoo.3oxxo.3ooxx. .....&#xt &   4 16 12 |  6 12  6 18  36 18 |  4  6 12  8 12 18  24  4 |  1  4  4  1  6  4  4 | *  * 10  *
.xo.. ..... .ox..3.oo..&#x  &   0  2  3 |  0  0  1  0   6  3 |  0  0  0  0  3  0   6  1 |  0  0  0  0  3  0  2 | *  *  * 20

© 2004-2019
top of page