Acronym | pedip |
Name | pentagon-pentagon duoprism |
© | |
Circumradius | sqrt[1+1/sqrt(5)] = 1.203002 |
Volume | [25+10 sqrt(5)]/16 = 2.960042 |
General of army | (is itself convex) |
Colonel of regiment | (is itself locally convex) |
Dihedral angles | |
Face vector | 25, 50, 35, 10 |
Confer |
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External links |
Note that pedip can be thought of as the external blend of 5 pippies + 5 pescs + 5 pafs. This decomposition is described as the degenerate segmentoteron ox5oo ox5xo&#xt.
Incidence matrix according to Dynkin symbol
x5o x5o . . . . | 25 | 2 2 | 1 4 1 | 2 2 --------+----+-------+--------+---- x . . . | 2 | 25 * | 1 2 0 | 2 1 . . x . | 2 | * 25 | 0 2 1 | 1 2 --------+----+-------+--------+---- x5o . . | 5 | 5 0 | 5 * * | 2 0 x . x . | 4 | 2 2 | * 25 * | 1 1 . . x5o | 5 | 0 5 | * * 5 | 0 2 --------+----+-------+--------+---- x5o x . ♦ 10 | 10 5 | 2 5 0 | 5 * x . x5o ♦ 10 | 5 10 | 0 5 2 | * 5
or . . . . | 25 | 4 | 2 4 | 4 -----------+----+----+-------+--- x . . . & | 2 | 50 | 1 2 | 3 -----------+----+----+-------+--- x5o . . & | 5 | 5 | 10 * | 2 x . x . | 4 | 4 | * 25 | 2 -----------+----+----+-------+--- x5o x . & ♦ 10 | 15 | 2 5 | 10
x5o x5/4o . . . . | 25 | 2 2 | 1 4 1 | 2 2 ----------+----+-------+--------+---- x . . . | 2 | 25 * | 1 2 0 | 2 1 . . x . | 2 | * 25 | 0 2 1 | 1 2 ----------+----+-------+--------+---- x5o . . | 5 | 5 0 | 5 * * | 2 0 x . x . | 4 | 2 2 | * 25 * | 1 1 . . x5/4o | 5 | 0 5 | * * 5 | 0 2 ----------+----+-------+--------+---- x5o x . ♦ 10 | 10 5 | 2 5 0 | 5 * x . x5/4o ♦ 10 | 5 10 | 0 5 2 | * 5
x5/4o x5/4o . . . . | 25 | 2 2 | 1 4 1 | 2 2 ------------+----+-------+--------+---- x . . . | 2 | 25 * | 1 2 0 | 2 1 . . x . | 2 | * 25 | 0 2 1 | 1 2 ------------+----+-------+--------+---- x5/4o . . | 5 | 5 0 | 5 * * | 2 0 x . x . | 4 | 2 2 | * 25 * | 1 1 . . x5/4o | 5 | 0 5 | * * 5 | 0 2 ------------+----+-------+--------+---- x5/4o x . ♦ 10 | 10 5 | 2 5 0 | 5 * x . x5/4o ♦ 10 | 5 10 | 0 5 2 | * 5
or . . . . | 25 | 4 | 2 4 | 4 ---------------+----+----+-------+--- x . . . & | 2 | 50 | 1 2 | 3 ---------------+----+----+-------+--- x5/4o . . & | 5 | 5 | 10 * | 2 x . x . | 4 | 4 | * 25 | 2 ---------------+----+----+-------+--- x5/4o x . & ♦ 10 | 15 | 2 5 | 10
ofx xxx5ooo&#xt → height(1,2) = sqrt[(5-sqrt(5))/8] = 0.587785 height(2,3) = sqrt[(5+sqrt(5))/8] = 0.951057 ({5} || pseudo (f,x)-pip || pip) o.. o..5o.. | 5 * * | 2 2 0 0 0 0 | 1 1 4 0 0 0 0 | 2 2 0 0 .o. .o.5.o. | * 10 * | 0 1 2 1 0 0 | 0 1 2 1 2 0 0 | 2 1 1 0 ..o ..o5..o | * * 10 | 0 0 0 1 1 2 | 0 1 0 0 2 2 1 | 2 0 1 1 ----------------+---------+-----------------+-----------------+-------- ... x.. ... | 2 0 0 | 5 * * * * * | 1 0 2 0 0 0 0 | 1 2 0 0 oo. oo.5oo.&#x | 1 1 0 | * 10 * * * * | 0 1 2 0 0 0 0 | 2 1 0 0 ... .x. ... | 0 2 0 | * * 10 * * * | 0 0 1 1 1 0 0 | 1 1 1 0 .oo .oo5.oo&#x | 0 1 1 | * * * 10 * * | 0 1 0 0 2 0 0 | 2 0 1 0 ..x ... ... | 0 0 2 | * * * * 5 * | 0 1 0 0 0 2 0 | 2 0 0 1 ... ..x ... | 0 0 2 | * * * * * 10 | 0 0 0 0 1 1 1 | 1 0 1 1 ----------------+---------+-----------------+-----------------+-------- ... x..5o.. | 5 0 0 | 5 0 0 0 0 0 | 1 * * * * * * | 0 2 0 0 ofx ... ...&#xt | 1 2 2 | 0 2 0 2 1 0 | * 5 * * * * * | 2 0 0 0 ... xx. ...&#x | 2 2 0 | 1 2 1 0 0 0 | * * 10 * * * * | 1 1 0 0 ... .x.5.o. | 0 5 0 | 0 0 5 0 0 0 | * * * 2 * * * | 0 1 1 0 ... .xx ...&#x | 0 2 2 | 0 0 1 2 0 1 | * * * * 10 * * | 1 0 1 0 ..x ..x ... | 0 0 4 | 0 0 0 0 2 2 | * * * * * 5 * | 1 0 0 1 ... ..x5..o | 0 0 5 | 0 0 0 0 0 5 | * * * * * * 2 | 0 0 1 1 ----------------+---------+-----------------+-----------------+-------- ofx xxx ...&#xt ♦ 2 4 4 | 1 4 2 4 2 2 | 0 2 2 0 2 1 0 | 5 * * * ... xx.5oo.&#x ♦ 5 5 0 | 5 5 5 0 0 0 | 1 0 5 1 0 0 0 | * 2 * * ... .xx5.oo&#x ♦ 0 5 5 | 0 0 5 5 0 5 | 0 0 0 1 5 0 1 | * * 2 * ..x ..x5..o ♦ 0 0 10 | 0 0 0 0 5 10 | 0 0 0 0 0 5 2 | * * * 1
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