Acronym | squipdip, K-4.42 |
Name | square-pentagon duoprism |
© | |
Circumradius | sqrt[(10+sqrt(5))/10] = 1.106168 |
Volume | sqrt[25+10 sqrt(5)]/4 = 1.720477 |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles | |
Face vector | 20, 40, 29, 9 |
Confer |
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External links |
As abstract polytope squipdip is isomorphic to sistadip, thereby replacing pentagons by pentagrams, resp. pip by stip.
Incidence matrix according to Dynkin symbol
x4o x5o . . . . | 20 | 2 2 | 1 4 1 | 2 2 --------+----+-------+--------+---- x . . . | 2 | 20 * | 1 2 0 | 2 1 . . x . | 2 | * 20 | 0 2 1 | 1 2 --------+----+-------+--------+---- x4o . . | 4 | 4 0 | 5 * * | 2 0 x . x . | 4 | 2 2 | * 20 * | 1 1 . . x5o | 5 | 0 5 | * * 4 | 0 2 --------+----+-------+--------+---- x4o x . ♦ 8 | 8 4 | 2 4 0 | 5 * x . x5o ♦ 10 | 5 10 | 0 5 2 | * 4
x4o x5/4o . . . . | 20 | 2 2 | 1 4 1 | 2 2 ----------+----+-------+--------+---- x . . . | 2 | 20 * | 1 2 0 | 2 1 . . x . | 2 | * 20 | 0 2 1 | 1 2 ----------+----+-------+--------+---- x4o . . | 4 | 4 0 | 5 * * | 2 0 x . x . | 4 | 2 2 | * 20 * | 1 1 . . x5/4o | 5 | 0 5 | * * 4 | 0 2 ----------+----+-------+--------+---- x4o x . ♦ 8 | 8 4 | 2 4 0 | 5 * x . x5/4o ♦ 10 | 5 10 | 0 5 2 | * 4
x4/3o x5o . . . . | 20 | 2 2 | 1 4 1 | 2 2 ----------+----+-------+--------+---- x . . . | 2 | 20 * | 1 2 0 | 2 1 . . x . | 2 | * 20 | 0 2 1 | 1 2 ----------+----+-------+--------+---- x4/3o . . | 4 | 4 0 | 5 * * | 2 0 x . x . | 4 | 2 2 | * 20 * | 1 1 . . x5o | 5 | 0 5 | * * 4 | 0 2 ----------+----+-------+--------+---- x4/3o x . ♦ 8 | 8 4 | 2 4 0 | 5 * x . x5o ♦ 10 | 5 10 | 0 5 2 | * 4
x4/3o x5/4o . . . . | 20 | 2 2 | 1 4 1 | 2 2 ------------+----+-------+--------+---- x . . . | 2 | 20 * | 1 2 0 | 2 1 . . x . | 2 | * 20 | 0 2 1 | 1 2 ------------+----+-------+--------+---- x4/3o . . | 4 | 4 0 | 5 * * | 2 0 x . x . | 4 | 2 2 | * 20 * | 1 1 . . x5/4o | 5 | 0 5 | * * 4 | 0 2 ------------+----+-------+--------+---- x4/3o x . ♦ 8 | 8 4 | 2 4 0 | 5 * x . x5/4o ♦ 10 | 5 10 | 0 5 2 | * 4
x x x5o . . . . | 20 | 1 1 2 | 1 2 2 1 | 2 1 1 --------+----+----------+-----------+------ x . . . | 2 | 10 * * | 1 2 0 0 | 2 1 0 . x . . | 2 | * 10 * | 1 0 2 0 | 2 0 1 . . x . | 2 | * * 20 | 0 1 1 1 | 1 1 1 --------+----+----------+-----------+------ x x . . | 4 | 2 2 0 | 5 * * * | 2 0 0 x . x . | 4 | 2 0 2 | * 10 * * | 1 1 0 . x x . | 4 | 0 2 2 | * * 10 * | 1 0 1 . . x5o | 5 | 0 0 5 | * * * 4 | 0 1 1 --------+----+----------+-----------+------ x x x . ♦ 8 | 4 4 4 | 2 2 2 0 | 5 * * x . x5o ♦ 10 | 5 0 10 | 0 5 0 2 | * 2 * . x x5o ♦ 10 | 0 5 10 | 0 0 5 2 | * * 2 snubbed forms: x2s2s5o
xx xx5oo&#x → height = 1
(pip || pip)
o. o.5o. | 10 * | 1 2 1 0 0 | 2 1 1 2 0 0 | 1 2 1 0
.o .o5.o | * 10 | 0 0 1 1 2 | 0 0 1 2 2 1 | 0 2 1 1
------------+-------+--------------+--------------+--------
x. .. .. | 2 0 | 5 * * * * | 2 0 1 0 0 0 | 1 2 0 0
.. x. .. | 2 0 | * 10 * * * | 1 1 0 1 0 0 | 1 1 1 0
oo oo5oo&#x | 1 1 | * * 10 * * | 0 0 1 2 0 0 | 0 2 1 0
.x .. .. | 0 2 | * * * 5 * | 0 0 1 0 2 0 | 0 2 0 1
.. .x .. | 0 2 | * * * * 10 | 0 0 0 1 1 1 | 0 1 1 1
------------+-------+--------------+--------------+--------
x. x. .. | 4 0 | 2 2 0 0 0 | 5 * * * * * | 1 1 0 0
.. x.5o. | 5 0 | 0 5 0 0 0 | * 2 * * * * | 1 0 1 0
xx .. ..&#x | 2 2 | 1 0 2 1 0 | * * 5 * * * | 0 2 0 0
.. xx ..&#x | 2 2 | 0 1 2 0 1 | * * * 10 * * | 0 1 1 0
.x .x .. | 0 4 | 0 0 0 2 2 | * * * * 5 * | 0 1 0 1
.. .x5.o | 0 5 | 0 0 0 0 5 | * * * * * 2 | 0 0 1 1
------------+-------+--------------+--------------+--------
x. x.5o. ♦ 10 0 | 5 10 0 0 0 | 5 2 0 0 0 0 | 1 * * *
xx xx ..&#x ♦ 4 4 | 2 2 4 2 2 | 1 0 2 2 1 0 | * 5 * *
.. xx5oo&#x ♦ 5 5 | 0 5 5 0 5 | 0 1 0 5 0 1 | * * 2 *
.x .x5.o ♦ 0 10 | 0 0 0 5 10 | 0 0 0 0 5 2 | * * * 1
ofx xxx4ooo&#xt → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785 height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057 ({4} || pseudo (f,x,x)-cube || cube) o.. o.. o.. | 4 * * | 2 2 0 0 0 0 | 1 1 2 2 0 0 0 | 2 2 0 0 .o. .o. .o. | * 8 * | 0 1 2 1 0 0 | 0 1 1 2 2 0 0 | 2 1 1 0 ..o ..o ..o | * * 8 | 0 0 0 1 1 2 | 0 1 0 0 2 2 1 | 2 0 1 1 ----------------+-------+-------------+---------------+-------- ... x.. ... | 2 0 0 | 4 * * * * * | 1 0 2 0 0 0 0 | 1 2 0 0 oo. oo.4oo.&#x | 1 1 0 | * 8 * * * * | 0 1 1 1 0 0 0 | 2 1 0 0 ... .x. ... | 0 2 0 | * * 8 * * * | 0 0 1 1 1 0 0 | 1 1 1 0 .oo .oo4.oo&#x | 0 1 1 | * * * 8 * * | 0 1 0 0 2 0 0 | 2 0 1 0 ..x ... ... | 0 0 2 | * * * * 4 * | 0 1 0 0 0 2 0 | 2 0 0 1 ... ..x ... | 0 0 2 | * * * * * 8 | 0 0 0 0 1 1 1 | 1 0 1 1 ----------------+-------+-------------+---------------+-------- ... x..4o.. | 4 0 0 | 4 0 0 0 0 0 | 1 * * * * * * | 0 2 0 0 ofx ... ...&#xt | 1 2 2 | 0 2 0 2 1 0 | * 4 * * * * * | 2 0 0 0 ... xx. ...&#x | 2 2 0 | 1 2 1 0 0 0 | * * 8 * * * * | 1 1 0 0 ... .x.4.o. | 0 4 0 | 0 0 4 0 0 0 | * * * 2 * * * | 0 1 1 0 ... .xx ...&#x | 0 2 2 | 0 0 1 2 0 1 | * * * * 8 * * | 1 0 1 0 ..x ..x ... | 0 0 4 | 0 0 0 0 2 2 | * * * * * 4 * | 1 0 0 1 ... ..x4..o | 0 0 4 | 0 0 0 0 0 4 | * * * * * * 2 | 0 0 1 1 ----------------+-------+-------------+---------------+-------- ofx xxx ...&#xt ♦ 2 4 4 | 1 4 2 4 2 2 | 0 2 2 0 2 1 0 | 4 * * * ... xx.4oo.&#x ♦ 4 4 0 | 4 4 4 0 0 0 | 1 0 4 1 0 0 0 | * 2 * * ... .xx4.oo&#x ♦ 0 4 4 | 0 0 4 4 0 4 | 0 0 0 1 4 0 1 | * * 2 * ..x ..x4..o ♦ 0 0 8 | 0 0 0 0 4 8 | 0 0 0 0 0 4 2 | * * * 1
ofx xxx xxx&#xt → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785 height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057 ({4} || pseudo (f,x,x)-cube || cube) o.. o.. o.. | 4 * * | 1 1 2 0 0 0 0 0 0 | 1 1 2 2 0 0 0 0 0 0 | 1 1 2 0 0 .o. .o. .o. | * 8 * | 0 0 1 1 1 1 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0 ..o ..o ..o | * * 8 | 0 0 0 0 0 1 1 1 1 | 0 1 0 0 0 1 1 1 1 1 | 1 1 0 1 1 ----------------+-------+-------------------+---------------------+---------- ... x.. ... | 2 0 0 | 2 * * * * * * * * | 1 0 2 0 0 0 0 0 0 0 | 1 0 2 0 0 ... ... x.. | 2 0 0 | * 2 * * * * * * * | 1 0 0 2 0 0 0 0 0 0 | 0 1 2 0 0 oo. oo. oo.&#x | 1 1 0 | * * 8 * * * * * * | 0 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0 ... .x. ... | 0 2 0 | * * * 4 * * * * * | 0 0 1 0 1 1 0 0 0 0 | 1 0 1 1 0 ... ... .x. | 0 2 0 | * * * * 4 * * * * | 0 0 0 1 1 0 1 0 0 0 | 0 1 1 1 0 .oo .oo .oo&#x | 0 1 1 | * * * * * 8 * * * | 0 1 0 0 0 1 1 0 0 0 | 1 1 0 1 0 ..x ... ... | 0 0 2 | * * * * * * 4 * * | 0 1 0 0 0 0 0 1 1 0 | 1 1 0 0 1 ... ..x ... | 0 0 2 | * * * * * * * 4 * | 0 0 0 0 0 1 0 1 0 1 | 1 0 0 1 1 ... ... ..x | 0 0 2 | * * * * * * * * 4 | 0 0 0 0 0 0 1 0 1 1 | 0 1 0 1 1 ----------------+-------+-------------------+---------------------+---------- ... x.. x.. | 4 0 0 | 2 2 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 0 0 2 0 0 ofx ... ...&#xt | 1 2 2 | 0 0 2 0 0 2 1 0 0 | * 4 * * * * * * * * | 1 1 0 0 0 ... xx. ...&#x | 2 2 0 | 1 0 2 1 0 0 0 0 0 | * * 4 * * * * * * * | 1 0 1 0 0 ... ... xx.&#x | 2 2 0 | 0 1 2 0 1 0 0 0 0 | * * * 4 * * * * * * | 0 1 1 0 0 ... .x. .x. | 0 4 0 | 0 0 0 2 2 0 0 0 0 | * * * * 2 * * * * * | 0 0 1 1 0 ... .xx ...&#x | 0 2 2 | 0 0 0 1 0 2 0 1 0 | * * * * * 4 * * * * | 1 0 0 1 0 ... ... .xx&#x | 0 2 2 | 0 0 0 0 1 2 0 0 1 | * * * * * * 4 * * * | 0 1 0 1 0 ..x ..x ... | 0 0 4 | 0 0 0 0 0 0 2 2 0 | * * * * * * * 2 * * | 1 0 0 0 1 ..x ... ..x | 0 0 4 | 0 0 0 0 0 0 2 0 2 | * * * * * * * * 2 * | 0 1 0 0 1 ... ..x ..x | 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * 2 | 0 0 0 1 1 ----------------+-------+-------------------+---------------------+---------- ofx xxx ...&#xt ♦ 2 4 4 | 1 0 4 2 0 4 2 2 0 | 0 2 2 0 0 2 0 1 0 0 | 2 * * * * ofx ... xxx&#xt ♦ 2 4 4 | 0 1 4 0 2 4 2 0 2 | 0 2 0 2 0 0 2 0 1 0 | * 2 * * * ... xx. xx.&#x ♦ 4 4 0 | 2 2 4 2 2 0 0 0 0 | 1 0 2 2 1 0 0 0 0 0 | * * 2 * * ... .xx .xx&#x ♦ 0 4 4 | 0 0 0 2 2 4 0 2 2 | 0 0 0 0 1 2 2 0 0 1 | * * * 2 * ..x ..x ..x ♦ 0 0 8 | 0 0 0 0 0 0 4 4 4 | 0 0 0 0 0 0 0 2 2 2 | * * * * 1
oqo xxx5ooo&#xt → both heights = 1/sqrt(2) = 0.707107 ({5} || pseudo (q,x)-pip || {5}) o.. o..5o.. & | 10 * | 2 2 0 | 1 1 4 0 | 2 2 .o. .o.5.o. | * 10 | 0 2 2 | 0 1 4 1 | 2 2 ------------------+-------+----------+----------+---- ... x.. ... & | 2 0 | 10 * * | 1 0 2 0 | 1 2 oo. oo.5oo.&#x & | 1 1 | * 20 * | 0 1 2 0 | 2 1 ... .x. ... | 0 2 | * * 10 | 0 0 2 1 | 1 2 ------------------+-------+----------+----------+---- ... x..5o.. & | 5 0 | 5 0 0 | 2 * * * | 0 2 oqo ... ...&#xt | 2 2 | 0 4 0 | * 5 * * | 2 0 ... xx. ...&#x & | 2 2 | 1 2 1 | * * 20 * | 1 1 ... .x.5.o. | 0 5 | 0 0 5 | * * * 2 | 0 2 ------------------+-------+----------+----------+---- oqo xxx ...&#xt ♦ 4 4 | 2 8 2 | 0 2 4 0 | 5 * ... xx.5oo.&#x & ♦ 5 5 | 5 5 5 | 1 0 5 1 | * 4
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