Acronym | stasc (old: stappypy) |
Name |
stellar scalene, pentagrammic scalene, pentagram-pyramidal pyramid, line atop fully orthogonal pentagram, 5 tet two-step rosette |
Circumradius | (sqrt(5)-1)/2 = 0.618034 |
Dual | (topologically selfdual, in different orientation) |
Dihedral angles | |
Face vector | 7, 16, 16, 7 |
Confer |
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External links |
As abstract polytope stasc is isomorphic to pesc, thereby replacing pentagrams by pentagons resp. replacing stappy by peppy.
Incidence matrix according to Dynkin symbol
oox5/2ooo&#x → height(1,2) = 1 height(1,3) = height(2,3) = sqrt((5+sqrt(5))/10) = 0.850651 o..5/2o.. | 1 * * ♦ 1 4 0 0 | 4 4 0 0 | 4 1 0 .o.5/2.o. | * 1 * ♦ 1 0 4 0 | 4 0 4 0 | 4 0 1 ..o5/2..o | * * 5 | 0 1 1 2 | 1 2 2 1 | 2 1 1 -------------+-------+---------+---------+------ oo.5/2oo.&#x | 1 1 0 | 1 * * * | 5 0 0 0 | 5 0 0 o.o5/2o.o&#x | 1 0 1 | * 5 * * | 1 2 0 0 | 2 1 0 .oo5/2.oo&#x | 0 1 1 | * * 5 * | 1 0 2 0 | 2 0 1 ..x ... | 0 0 2 | * * * 5 | 0 1 1 1 | 1 1 1 -------------+-------+---------+---------+------ ooo5/2ooo&#x | 1 1 1 | 1 1 1 0 | 5 * * * | 2 0 0 o.x ...&#x | 1 0 2 | 0 2 0 1 | * 5 * * | 1 1 0 .ox ...&#x | 0 1 2 | 0 0 2 1 | * * 5 * | 1 0 1 ..x5/2..o | 0 0 5 | 0 0 0 5 | * * * 1 | 0 1 1 -------------+-------+---------+---------+------ oox ...&#x ♦ 1 1 2 | 1 2 2 1 | 2 1 1 0 | 5 * * o.x5/2o.o&#x ♦ 1 0 5 | 0 5 0 5 | 0 5 0 1 | * 1 * .ox5/2.oo&#x ♦ 0 1 5 | 0 0 5 5 | 0 0 5 1 | * * 1
pt || stappy → height = (1+sqrt(5))/4 = 0.809017
o..5/2o.. | 1 * * ♦ 1 4 0 0 | 4 4 0 0 | 4 1 0
.o.5/2.o. | * 1 * ♦ 1 0 4 0 | 4 0 4 0 | 4 0 1
..o5/2..o | * * 5 | 0 1 1 2 | 1 2 2 1 | 2 1 1
-------------+-------+---------+---------+------
oo.5/2oo.&#x | 1 1 0 | 1 * * * | 5 0 0 0 | 5 0 0
o.o5/2o.o&#x | 1 0 1 | * 5 * * | 1 2 0 0 | 2 1 0
.oo5/2.oo&#x | 0 1 1 | * * 5 * | 1 0 2 0 | 2 0 1
..x ... | 0 0 2 | * * * 5 | 0 1 1 1 | 1 1 1
-------------+-------+---------+---------+------
ooo5/2ooo&#x | 1 1 1 | 1 1 1 0 | 5 * * * | 2 0 0
o.x ...&#x | 1 0 2 | 0 2 0 1 | * 5 * * | 1 1 0
.ox ...&#x | 0 1 2 | 0 0 2 1 | * * 5 * | 1 0 1
..x5/2..o | 0 0 5 | 0 0 0 5 | * * * 1 | 0 1 1
-------------+-------+---------+---------+------
oox ...&#x ♦ 1 1 2 | 1 2 2 1 | 2 1 1 0 | 5 * *
o.x5/2o.o&#x ♦ 1 0 5 | 0 5 0 5 | 0 5 0 1 | * 1 *
.ox5/2.oo&#x ♦ 0 1 5 | 0 0 5 5 | 0 0 5 1 | * * 1
pyramid product of line with {5/2} → height = sqrt[(5+2 sqrt(5))/20] = 0.688191 o..5/2o.. & | 2 * ♦ 1 4 0 | 4 4 0 | 4 1 ..o5/2..o | * 5 | 0 2 2 | 1 4 1 | 2 2 ----------------+-----+--------+--------+---- oo.5/2oo.&#x | 2 0 | 1 * * | 5 0 0 | 5 0 o.o5/2o.o&#x & | 1 1 | * 10 * | 1 2 0 | 2 1 ..x ... | 0 2 | * * 5 | 0 2 1 | 1 2 ----------------+-----+--------+--------+---- ooo5/2ooo&#x | 2 1 | 1 2 0 | 5 * * | 2 0 o.x ...&#x & | 1 2 | 0 2 1 | * 10 * | 1 1 ..x5/2..o | 0 5 | 0 0 5 | * * 1 | 0 2 ----------------+-----+--------+--------+---- oox ...&#x ♦ 2 2 | 1 4 1 | 2 2 0 | 5 * o.x5/2o.o&#x & ♦ 1 5 | 0 5 5 | 0 5 1 | * 2
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