| Acronym | sirpin |
| Name | small retroprismated penteract |
| Circumradius | sqrt(2)+1/2 = 1.914214 |
| Coordinates | (1+sqrt(2), 1+sqrt(2), 1, 1, 1)/2 & all permutations, all changes of sign |
| General of army | span |
| Colonel of regiment | span |
| Face vector | 320, 1440, 1440, 480, 52 |
| Confer |
|
As abstract polytope sirpin is isomorphic to fawdint, thereby replacing octagons by octagrams, resp. tic by quith and socco by gocco, resp. steth by gittith and rawvatoth by wavitoth. – As such sirpin is a lieutenant.
Incidence matrix according to Dynkin symbol
3 3 3
o---x---o---o
4 \ / 4/3
x
o3x3o3o *b4x4/3*c . . . . . | 320 | 6 3 | 3 6 6 3 | 3 3 2 6 1 | 1 3 2 ------------------+-----+---------+-----------------+------------------+--------- . x . . . | 2 | 960 * | 1 2 1 0 | 2 1 1 2 0 | 1 2 1 . . . . x | 2 | * 480 | 0 0 2 2 | 0 1 0 4 1 | 0 2 2 ------------------+-----+---------+-----------------+------------------+--------- o3x . . . | 3 | 3 0 | 320 * * * | 2 1 0 0 0 | 1 2 0 . x3o . . | 3 | 3 0 | * 640 * * | 1 0 1 1 0 | 1 1 1 . x . . *b4x | 8 | 4 4 | * * 240 * | 0 1 0 2 0 | 0 2 1 . . o . x4/3*c | 4 | 0 4 | * * * 240 | 0 0 0 2 1 | 0 1 2 ------------------+-----+---------+-----------------+------------------+--------- o3x3o . . ♦ 6 | 12 0 | 4 4 0 0 | 160 * * * * | 1 1 0 o3x . . *b4x ♦ 24 | 24 12 | 8 0 6 0 | * 40 * * * | 0 2 0 . x3o3o . ♦ 4 | 6 0 | 0 4 0 0 | * * 160 * * | 1 0 1 . x3o . *b4x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 80 * | 0 1 1 . . o3o x4/3*c ♦ 8 | 0 12 | 0 0 0 6 | * * * * 40 | 0 0 2 ------------------+-----+---------+-----------------+------------------+--------- o3x3o3o . ♦ 10 | 30 0 | 10 20 0 0 | 5 0 5 0 0 | 32 * * o3x3o . *b4x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 16 8 0 8 0 | * 10 * . x3o3o *b4x4/3*c ♦ 64 | 96 96 | 0 64 24 48 | 0 0 16 8 8 | * * 10
3 3 3/2
o---x---o---o
4 \ / 4/3
x
o3x3o3/2o *b4x4/3*c . . . . . | 320 | 6 3 | 3 6 6 3 | 3 3 2 6 1 | 1 3 2 --------------------+-----+---------+-----------------+------------------+--------- . x . . . | 2 | 960 * | 1 2 1 0 | 2 1 1 2 0 | 1 2 1 . . . . x | 2 | * 480 | 0 0 2 2 | 0 1 0 4 1 | 0 2 2 --------------------+-----+---------+-----------------+------------------+--------- o3x . . . | 3 | 3 0 | 320 * * * | 2 1 0 0 0 | 1 2 0 . x3o . . | 3 | 3 0 | * 640 * * | 1 0 1 1 0 | 1 1 1 . x . . *b4x | 8 | 4 4 | * * 240 * | 0 1 0 2 0 | 0 2 1 . . o . x4/3*c | 4 | 0 4 | * * * 240 | 0 0 0 2 1 | 0 1 2 --------------------+-----+---------+-----------------+------------------+--------- o3x3o . . ♦ 6 | 12 0 | 4 4 0 0 | 160 * * * * | 1 1 0 o3x . . *b4x ♦ 24 | 24 12 | 8 0 6 0 | * 40 * * * | 0 2 0 . x3o3/2o . ♦ 4 | 6 0 | 0 4 0 0 | * * 160 * * | 1 0 1 . x3o . *b4x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 80 * | 0 1 1 . . o3/2o x4/3*c ♦ 8 | 0 12 | 0 0 0 6 | * * * * 40 | 0 0 2 --------------------+-----+---------+-----------------+------------------+--------- o3x3o3/2o . ♦ 10 | 30 0 | 10 20 0 0 | 5 0 5 0 0 | 32 * * o3x3o . *b4x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 16 8 0 8 0 | * 10 * . x3o3/2o *b4x4/3*c ♦ 64 | 96 96 | 0 64 24 48 | 0 0 16 8 8 | * * 10
3/2 3 3
o---x---o---o
4 \ / 4/3
x
o3/2x3o3o *b4x4/3*c . . . . . | 320 | 6 3 | 3 6 6 3 | 3 3 2 6 1 | 1 3 2 --------------------+-----+---------+-----------------+------------------+--------- . x . . . | 2 | 960 * | 1 2 1 0 | 2 1 1 2 0 | 1 2 1 . . . . x | 2 | * 480 | 0 0 2 2 | 0 1 0 4 1 | 0 2 2 --------------------+-----+---------+-----------------+------------------+--------- o3/2x . . . | 3 | 3 0 | 320 * * * | 2 1 0 0 0 | 1 2 0 . x3o . . | 3 | 3 0 | * 640 * * | 1 0 1 1 0 | 1 1 1 . x . . *b4x | 8 | 4 4 | * * 240 * | 0 1 0 2 0 | 0 2 1 . . o . x4/3*c | 4 | 0 4 | * * * 240 | 0 0 0 2 1 | 0 1 2 --------------------+-----+---------+-----------------+------------------+--------- o3/2x3o . . ♦ 6 | 12 0 | 4 4 0 0 | 160 * * * * | 1 1 0 o3/2x . . *b4x ♦ 24 | 24 12 | 8 0 6 0 | * 40 * * * | 0 2 0 . x3o3o . ♦ 4 | 6 0 | 0 4 0 0 | * * 160 * * | 1 0 1 . x3o . *b4x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 80 * | 0 1 1 . . o3o x4/3*c ♦ 8 | 0 12 | 0 0 0 6 | * * * * 40 | 0 0 2 --------------------+-----+---------+-----------------+------------------+--------- o3/2x3o3o . ♦ 10 | 30 0 | 10 20 0 0 | 5 0 5 0 0 | 32 * * o3/2x3o . *b4x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 16 8 0 8 0 | * 10 * . x3o3o *b4x4/3*c ♦ 64 | 96 96 | 0 64 24 48 | 0 0 16 8 8 | * * 10
3/2 3 3/2
o---x---o---o
4 \ / 4/3
x
o3/2x3o3/2o *b4x4/3*c . . . . . | 320 | 6 3 | 3 6 6 3 | 3 3 2 6 1 | 1 3 2 ----------------------+-----+---------+-----------------+------------------+--------- . x . . . | 2 | 960 * | 1 2 1 0 | 2 1 1 2 0 | 1 2 1 . . . . x | 2 | * 480 | 0 0 2 2 | 0 1 0 4 1 | 0 2 2 ----------------------+-----+---------+-----------------+------------------+--------- o3/2x . . . | 3 | 3 0 | 320 * * * | 2 1 0 0 0 | 1 2 0 . x3o . . | 3 | 3 0 | * 640 * * | 1 0 1 1 0 | 1 1 1 . x . . *b4x | 8 | 4 4 | * * 240 * | 0 1 0 2 0 | 0 2 1 . . o . x4/3*c | 4 | 0 4 | * * * 240 | 0 0 0 2 1 | 0 1 2 ----------------------+-----+---------+-----------------+------------------+--------- o3/2x3o . . ♦ 6 | 12 0 | 4 4 0 0 | 160 * * * * | 1 1 0 o3/2x . . *b4x ♦ 24 | 24 12 | 8 0 6 0 | * 40 * * * | 0 2 0 . x3o3/2o . ♦ 4 | 6 0 | 0 4 0 0 | * * 160 * * | 1 0 1 . x3o . *b4x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 80 * | 0 1 1 . . o3/2o x4/3*c ♦ 8 | 0 12 | 0 0 0 6 | * * * * 40 | 0 0 2 ----------------------+-----+---------+-----------------+------------------+--------- o3/2x3o3/2o . ♦ 10 | 30 0 | 10 20 0 0 | 5 0 5 0 0 | 32 * * o3/2x3o . *b4x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 16 8 0 8 0 | * 10 * . x3o3/2o *b4x4/3*c ♦ 64 | 96 96 | 0 64 24 48 | 0 0 16 8 8 | * * 10
3 3/2 3
o---x---o---o
4 \ / 4
x
o3x3/2o3o *b4x4*c . . . . . | 320 | 6 3 | 3 6 6 3 | 3 3 2 6 1 | 1 3 2 ------------------+-----+---------+-----------------+------------------+--------- . x . . . | 2 | 960 * | 1 2 1 0 | 2 1 1 2 0 | 1 2 1 . . . . x | 2 | * 480 | 0 0 2 2 | 0 1 0 4 1 | 0 2 2 ------------------+-----+---------+-----------------+------------------+--------- o3x . . . | 3 | 3 0 | 320 * * * | 2 1 0 0 0 | 1 2 0 . x3/2o . . | 3 | 3 0 | * 640 * * | 1 0 1 1 0 | 1 1 1 . x . . *b4x | 8 | 4 4 | * * 240 * | 0 1 0 2 0 | 0 2 1 . . o . x4*c | 4 | 0 4 | * * * 240 | 0 0 0 2 1 | 0 1 2 ------------------+-----+---------+-----------------+------------------+--------- o3x3/2o . . ♦ 6 | 12 0 | 4 4 0 0 | 160 * * * * | 1 1 0 o3x . . *b4x ♦ 24 | 24 12 | 8 0 6 0 | * 40 * * * | 0 2 0 . x3/2o3o . ♦ 4 | 6 0 | 0 4 0 0 | * * 160 * * | 1 0 1 . x3/2o . *b4x4*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 80 * | 0 1 1 . . o3o x4*c ♦ 8 | 0 12 | 0 0 0 6 | * * * * 40 | 0 0 2 ------------------+-----+---------+-----------------+------------------+--------- o3x3/2o3o . ♦ 10 | 30 0 | 10 20 0 0 | 5 0 5 0 0 | 32 * * o3x3/2o . *b4x4*c ♦ 96 | 192 96 | 64 64 48 24 | 16 8 0 8 0 | * 10 * . x3/2o3o *b4x4*c ♦ 64 | 96 96 | 0 64 24 48 | 0 0 16 8 8 | * * 10
3 3/2 3/2
o---x---o---o
4 \ / 4
x
o3x3/2o3/2o *b4x4*c . . . . . | 320 | 6 3 | 3 6 6 3 | 3 3 2 6 1 | 1 3 2 --------------------+-----+---------+-----------------+------------------+--------- . x . . . | 2 | 960 * | 1 2 1 0 | 2 1 1 2 0 | 1 2 1 . . . . x | 2 | * 480 | 0 0 2 2 | 0 1 0 4 1 | 0 2 2 --------------------+-----+---------+-----------------+------------------+--------- o3x . . . | 3 | 3 0 | 320 * * * | 2 1 0 0 0 | 1 2 0 . x3/2o . . | 3 | 3 0 | * 640 * * | 1 0 1 1 0 | 1 1 1 . x . . *b4x | 8 | 4 4 | * * 240 * | 0 1 0 2 0 | 0 2 1 . . o . x4*c | 4 | 0 4 | * * * 240 | 0 0 0 2 1 | 0 1 2 --------------------+-----+---------+-----------------+------------------+--------- o3x3/2o . . ♦ 6 | 12 0 | 4 4 0 0 | 160 * * * * | 1 1 0 o3x . . *b4x ♦ 24 | 24 12 | 8 0 6 0 | * 40 * * * | 0 2 0 . x3/2o3/2o . ♦ 4 | 6 0 | 0 4 0 0 | * * 160 * * | 1 0 1 . x3/2o . *b4x4*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 80 * | 0 1 1 . . o3/2o x4*c ♦ 8 | 0 12 | 0 0 0 6 | * * * * 40 | 0 0 2 --------------------+-----+---------+-----------------+------------------+--------- o3x3/2o3/2o . ♦ 10 | 30 0 | 10 20 0 0 | 5 0 5 0 0 | 32 * * o3x3/2o . *b4x4*c ♦ 96 | 192 96 | 64 64 48 24 | 16 8 0 8 0 | * 10 * . x3/2o3/2o *b4x4*c ♦ 64 | 96 96 | 0 64 24 48 | 0 0 16 8 8 | * * 10
3/2 3/2 3
o---x---o---o
4 \ / 4
x
o3/2x3/2o3o *b4x4*c . . . . . | 320 | 6 3 | 3 6 6 3 | 3 3 2 6 1 | 1 3 2 --------------------+-----+---------+-----------------+------------------+--------- . x . . . | 2 | 960 * | 1 2 1 0 | 2 1 1 2 0 | 1 2 1 . . . . x | 2 | * 480 | 0 0 2 2 | 0 1 0 4 1 | 0 2 2 --------------------+-----+---------+-----------------+------------------+--------- o3/2x . . . | 3 | 3 0 | 320 * * * | 2 1 0 0 0 | 1 2 0 . x3/2o . . | 3 | 3 0 | * 640 * * | 1 0 1 1 0 | 1 1 1 . x . . *b4x | 8 | 4 4 | * * 240 * | 0 1 0 2 0 | 0 2 1 . . o . x4*c | 4 | 0 4 | * * * 240 | 0 0 0 2 1 | 0 1 2 --------------------+-----+---------+-----------------+------------------+--------- o3/2x3/2o . . ♦ 6 | 12 0 | 4 4 0 0 | 160 * * * * | 1 1 0 o3/2x . . *b4x ♦ 24 | 24 12 | 8 0 6 0 | * 40 * * * | 0 2 0 . x3/2o3o . ♦ 4 | 6 0 | 0 4 0 0 | * * 160 * * | 1 0 1 . x3/2o . *b4x4*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 80 * | 0 1 1 . . o3o x4*c ♦ 8 | 0 12 | 0 0 0 6 | * * * * 40 | 0 0 2 --------------------+-----+---------+-----------------+------------------+--------- o3/2x3/2o3o . ♦ 10 | 30 0 | 10 20 0 0 | 5 0 5 0 0 | 32 * * o3/2x3/2o . *b4x4*c ♦ 96 | 192 96 | 64 64 48 24 | 16 8 0 8 0 | * 10 * . x3/2o3o *b4x4*c ♦ 64 | 96 96 | 0 64 24 48 | 0 0 16 8 8 | * * 10
3/2 3/2 3/2
o---x---o---o
4 \ / 4
x
o3/2x3/2o3/2o *b4x4*c . . . . . | 320 | 6 3 | 3 6 6 3 | 3 3 2 6 1 | 1 3 2 ----------------------+-----+---------+-----------------+------------------+--------- . x . . . | 2 | 960 * | 1 2 1 0 | 2 1 1 2 0 | 1 2 1 . . . . x | 2 | * 480 | 0 0 2 2 | 0 1 0 4 1 | 0 2 2 ----------------------+-----+---------+-----------------+------------------+--------- o3/2x . . . | 3 | 3 0 | 320 * * * | 2 1 0 0 0 | 1 2 0 . x3/2o . . | 3 | 3 0 | * 640 * * | 1 0 1 1 0 | 1 1 1 . x . . *b4x | 8 | 4 4 | * * 240 * | 0 1 0 2 0 | 0 2 1 . . o . x4*c | 4 | 0 4 | * * * 240 | 0 0 0 2 1 | 0 1 2 ----------------------+-----+---------+-----------------+------------------+--------- o3/2x3/2o . . ♦ 6 | 12 0 | 4 4 0 0 | 160 * * * * | 1 1 0 o3/2x . . *b4x ♦ 24 | 24 12 | 8 0 6 0 | * 40 * * * | 0 2 0 . x3/2o3/2o . ♦ 4 | 6 0 | 0 4 0 0 | * * 160 * * | 1 0 1 . x3/2o . *b4x4*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 80 * | 0 1 1 . . o3/2o x4*c ♦ 8 | 0 12 | 0 0 0 6 | * * * * 40 | 0 0 2 ----------------------+-----+---------+-----------------+------------------+--------- o3/2x3/2o3/2o . ♦ 10 | 30 0 | 10 20 0 0 | 5 0 5 0 0 | 32 * * o3/2x3/2o . *b4x4*c ♦ 96 | 192 96 | 64 64 48 24 | 16 8 0 8 0 | * 10 * . x3/2o3/2o *b4x4*c ♦ 64 | 96 96 | 0 64 24 48 | 0 0 16 8 8 | * * 10
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