Will it ambigram?

Question

First challenge!

What is an ambigram?

Ambigrams are word(s) that read the same word(s) or another word given a certain transformation and possibly stylistic alterations.

Example:

That's an example of a rotational ambigram; it reads the same word, even when flipped around.

The Challenge

You are to create a function, program, etc. that can detect whether a given input (consisting of only a-zA-Z chars) is a natural symmetric ambigram (an ambigram that reads the same word without significant artistic alteration given a transformation). You can compete in one or more of the following categories:

Rotational

Examples: I, O, ae, AV, pod

Transformation table (both ways)

a  e/D
b  q
d  p/P
h  y
l  l
m  w
n  u/U
o  o/O/G/Q
s  s/S
t  t
x  x/X
z  z/Z
A  v/V
B  E
D  G
H  H
I  I
M  W
N  N

Output truesy or falsy value.

Reflectional (Vertical Line)

Examples: wow, mom, HOH

Chars to match

b/d i j l m n o p/q s/z t u v w x y A B/E G/D H I M O Q S/Z T U V W X Y

Output truthy or falsy value.

Reflectional (Horizontal Line)

Examples: XOD, KEK, BED

Chars to match

a l o t x B C D E H I K O X

Output truthy or falsy value.

Totem

Examples:

x  n  O
o  u  H
x  M  I
      O

Chars to match

A H I M O T U V W X Y i l m n o t u v w x y

Output truthy or falsy value.

Any (bonus of -50%)

This code should either output the type(s) of ambigram(s) that the input could possibly be (if the input is an ambigram) or a falsy value (if the input is not an ambigram).

Code rules

• Standard loopholes are disallowed.
• Input is case-sensitive. This means that AV would count, but aV would not count as a rotational ambigram.
• An input of zero length is considered to be a natural symmetric ambigram.
• Make sure to write your header as: # Division, Language, Byte-Count.
• This is code-golf! You know what that means.

Answer 1

Python 2, 258 bytes (622 567 543 516-50%)

Here's my attempt at an answer.

R=dict(zip(list('abdhlmnostxzABDHIMN'),'eD q pP y l w uU oOGQ sS t xX zZ vV E G H I W N'.split()))
V='ijlmnotuvwxyAHIMOQTUVWXY'
W=dict(b='d',p='q',s='z',B='E',G='D',S='Z')
H='lotxBCDEHIKOX'
T='AHIMOTUVWXYilmnotuvwxy'
s=raw_input()
r=v=h=t=1
for i,j in R.items():
 for c in j:R[c]=R.get(c,'')+i
for i,j in W.items():
 for c in j:W[c]=W.get(c,'')+i
for i in range(len(s)):
 c,l=s[i],s[-i-1]
 r&=(c in R and l in R[c])
 v&=c in V or(c in W and l in W[c])
 h&=(c in H)+(l in H)>1
 t&=c in T
print 'R'*r+'V'*v+'H'*h+'T'*t

Prints the possible types of ambigrams, or 0 if no ambigrams are possible.

RVHT for rotational, vertical, horizontal and totem respectively.

Answer 2

All, Ruby, 289 - 50% = 144.5 bytes

i=gets.chop;s=i.tr('ijlmnotuvwxyAHIMOQTUVWXY','').tr'bpsBGS','dqzEDZ';t=i.tr'eDqpPylwuUOGQStXZvVEGHIWN','aabddhlmnnooostxzAABDHIMN';o=(i.tr('alotxBCDEHIKOX','')=='' ? 'V':'')+(s==s.reverse ? 'H':'')+(i.tr('AHIMOUVWXYilmnotuvwxy','')=='' ? 'T':'')+(t==t.reverse ? 'R':'');puts o=='' ? 1<0:o

This seems too long...